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Journal articles on the topic 'Ring theory'

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Published: 4 June 2021
Last updated: 6 September 2023

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1

Baker, Ron. "Ring theory." New Scientist 217, no. 2898 (January 2013): 27. http://dx.doi.org/10.1016/s0262-4079(13)60045-7.

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2

Goldman, Michael A. "Ring theory." Nature 432, no. 7018 (December 2004): 674–75. http://dx.doi.org/10.1038/432674b.

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3

Matson, John. "Ring Theory." Scientific American 308, no. 2 (January 14, 2013): 15. http://dx.doi.org/10.1038/scientificamerican0213-15a.

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4

Xue, Zeqi. "Group Theory and Ring Theory." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012024. http://dx.doi.org/10.1088/1742-6596/2386/1/012024.

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Abstract Group theory is an important theory in abstract algebra. A ring is a kind of algebraic system with two operations (addition and multiplication). It has a deep relationship with groups, especially with the Abelian group. In this essay, the ring and the residual class ring will be talked about. Firstly, this passage is aim to talk about some basic knowledge about the ring which will let readers have a basic understanding of a ring. Then this passage will discuss the residual class ring and subring of the residual class ring of modulo. Some concepts about the ring are also mentioned, such as the centre of the ring, the identity of the ring, the classification of a ring, the residual class ring, the field and the zero divisors. The definitions of mathematical terms mentioned before are stated, as well as some examples of the part of those terms are given. In this passage, there are also some lemmas which are the properties of ring and subring. Future studies of rings and subrings can focus on the application of physics.
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5

Kozhukhov, I. B. "Technique of semigroup ring theory: Regular semigroup rings." Journal of Mathematical Sciences 95, no. 4 (July 1999): 2317–27. http://dx.doi.org/10.1007/bf02169100.

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6

Formanek, Edward. "Book Review: Ring theory." Bulletin of the American Mathematical Society 20, no. 2 (April 1, 1989): 196–99. http://dx.doi.org/10.1090/s0273-0979-1989-15762-5.

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7

Michel, F. Curtis. "Planetary Ring: Another Theory." Physics Today 40, no. 10 (October 1987): 160–62. http://dx.doi.org/10.1063/1.2820253.

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8

Rota, Gian-Carlo. "Dimensions of ring theory." Advances in Mathematics 71, no. 1 (September 1988): 131. http://dx.doi.org/10.1016/0001-8708(88)90074-6.

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9

Elleaume, P. "Storage ring FEL theory." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 237, no. 1-2 (June 1985): 28–37. http://dx.doi.org/10.1016/0168-9002(85)90326-2.

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10

Richardson, Jeremy O. "Ring-polymer instanton theory." International Reviews in Physical Chemistry 37, no. 2 (April 3, 2018): 171–216. http://dx.doi.org/10.1080/0144235x.2018.1472353.

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11

Kuiken, H. K., E. P. A. M. Bakkers, H. Ligthart, and J. J. Kelly. "The Rotating Ring-Ring Electrode. Theory and Experiment." Journal of The Electrochemical Society 147, no. 3 (2000): 1110. http://dx.doi.org/10.1149/1.1393321.

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12

Jung, Da Woon, Tai Keun Kwak, Min Jung Lee, and Yang Lee. "Ring properties related to symmetric rings." International Journal of Algebra and Computation 24, no. 07 (November 2014): 935–67. http://dx.doi.org/10.1142/s0218196714500428.

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The study of symmetric rings has important roles in ring theory and module theory. We investigate the structure of ring properties related to symmetric rings and introduce H-symmetric and π-symmetric as generalizations. We construct a non-symmetric reversible ring whose basic structure is infinite-dimensional, comparing with the finite-dimensional such rings of Anderson, Camillo and Marks. The structure of π-reversible rings (with or without identity) of minimal order is completely investigated. The properties of zero-dividing polynomials over IFP rings are studied more to show that polynomial rings over symmetric rings are π-symmetric. It is also proved that all conditions in relation with our arguments in this paper are equivalent for regular or locally finite rings.
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13

Tunc¸ay, Mesut, and Aslihan Sezgin. "Soft Union Ring and its Applications to Ring Theory." International Journal of Computer Applications 151, no. 9 (October 17, 2016): 7–13. http://dx.doi.org/10.5120/ijca2016911867.

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14

Carboni, Graciela, Jorge A. Guccione, and Juan J. Guccione. "Cohomology ring of differential operator rings." Journal of Algebra 339, no. 1 (August 2011): 55–79. http://dx.doi.org/10.1016/j.jalgebra.2011.05.017.

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15

Barnard, Tony, and P. M. Cohn. "An Introduction to Ring Theory." Mathematical Gazette 85, no. 503 (July 2001): 362. http://dx.doi.org/10.2307/3622065.

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16

Zelikin, M. I. "Fractal theory of Saturn’s ring." Proceedings of the Steklov Institute of Mathematics 291, no. 1 (November 2015): 87–101. http://dx.doi.org/10.1134/s008154381508009x.

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17

Farkas, Daniel R., and Gail Letzter. "Ring theory from symplectic geometry." Journal of Pure and Applied Algebra 125, no. 1-3 (March 1998): 155–90. http://dx.doi.org/10.1016/s0022-4049(96)00117-x.

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18

Okayama, Hideaki. "Ring Light Beam Deflector: Theory." Optical Review 10, no. 4 (July 2003): 283–86. http://dx.doi.org/10.1007/s10043-003-0283-5.

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19

Zhang, Jianluo, and John W. Y. Lit. "Compound fiber ring resonator: theory." Journal of the Optical Society of America A 11, no. 6 (June 1, 1994): 1867. http://dx.doi.org/10.1364/josaa.11.001867.

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20

Richardson, Jeremy O. "Perspective: Ring-polymer instanton theory." Journal of Chemical Physics 148, no. 20 (May 28, 2018): 200901. http://dx.doi.org/10.1063/1.5028352.

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21

Boeyens, J. C. A., and D. G. Evans. "Group theory of ring pucker." Acta Crystallographica Section B Structural Science 45, no. 6 (December 1, 1989): 577–81. http://dx.doi.org/10.1107/s0108768189008189.

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22

Ding, Nanqing, Tai Keun Kwak, Fang Li, and Masahisa Sato. "Ring Theory and Related Topics." Frontiers of Mathematics in China 11, no. 4 (July 4, 2016): 763–64. http://dx.doi.org/10.1007/s11464-016-0568-1.

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23

Banaschewski, B. "Ring theory and pointfree topology." Topology and its Applications 137, no. 1-3 (February 2004): 21–37. http://dx.doi.org/10.1016/s0166-8641(03)00196-2.

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24

Martinelli, Massimo, and Joseph C. Palais. "Theory of a tunable fiber ring depolarizer theory." Applied Optics 40, no. 18 (June 20, 2001): 3014. http://dx.doi.org/10.1364/ao.40.003014.

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25

Kleiner, Israel. "From Numbers to Rings: The Early History of Ring Theory." Elemente der Mathematik 53, no. 1 (February 1, 1998): 18–35. http://dx.doi.org/10.1007/s000170050029.

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26

Bakuradze, Malkhaz, and Mamuka Jibladze. "MoravaK-theory rings for the groupsG38, …,G41of order 32." Journal of K-Theory 13, no. 1 (December 6, 2013): 171–98. http://dx.doi.org/10.1017/is013011009jkt245.

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AbstractB. Schuster [19] proved that themod2 MoravaK-theoryK(s)*(BG) is evenly generated for all groupsGof order 32. For the four groupsGof order 32 with the numbers 38, 39, 40 and 41 in the Hall-Senior list [11], the ringK(2)*(BG) has been shown to be generated as aK(2)*-module by transferred Euler classes. In this paper, we show this for arbitrarysand compute the ring structure ofK(s)*(BG). Namely, we show thatK(s)*(BG) is the quotient of a polynomial ring in 6 variables overK(s)*(pt) by an ideal for which we list explicit generators.
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27

Groechenig, Michael. "Adelic descent theory." Compositio Mathematica 153, no. 8 (May 31, 2017): 1706–46. http://dx.doi.org/10.1112/s0010437x17007217.

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A result of André Weil allows one to describe rank $n$ vector bundles on a smooth complete algebraic curve up to isomorphism via a double quotient of the set $\text{GL}_{n}(\mathbb{A})$ of regular matrices over the ring of adèles (over algebraically closed fields, this result is also known to extend to $G$-torsors for a reductive algebraic group $G$). In the present paper we develop analogous adelic descriptions for vector and principal bundles on arbitrary Noetherian schemes, by proving an adelic descent theorem for perfect complexes. We show that for Beilinson’s co-simplicial ring of adèles $\mathbb{A}_{X}^{\bullet }$, we have an equivalence $\mathsf{Perf}(X)\simeq |\mathsf{Perf}(\mathbb{A}_{X}^{\bullet })|$ between perfect complexes on $X$ and cartesian perfect complexes for $\mathbb{A}_{X}^{\bullet }$. Using the Tannakian formalism for symmetric monoidal $\infty$-categories, we conclude that a Noetherian scheme can be reconstructed from the co-simplicial ring of adèles. We view this statement as a scheme-theoretic analogue of Gelfand–Naimark’s reconstruction theorem for locally compact topological spaces from their ring of continuous functions. Several results for categories of perfect complexes over (a strong form of) flasque sheaves of algebras are established, which might be of independent interest.
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28

Geiger, Joel, and Milen Yakimov. "Quantum Schubert cells via representation theory and ring theory." Michigan Mathematical Journal 63, no. 1 (March 2014): 125–57. http://dx.doi.org/10.1307/mmj/1395234362.

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29

Gálvez-Carrillo, Imma, and Sarah Whitehouse. "Central Cohomology Operations and K-Theory." Proceedings of the Edinburgh Mathematical Society 57, no. 3 (April 16, 2014): 699–711. http://dx.doi.org/10.1017/s0013091513000680.

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AbstractFor stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP〈n⌰ for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.
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30

Warren, Roger D. "The freeA-ring is a gradedA-ring." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 617–19. http://dx.doi.org/10.1155/s0161171293000766.

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31

del Río, A. "Categorical methods in graded ring theory." Publicacions Matemàtiques 36 (July 1, 1992): 489–531. http://dx.doi.org/10.5565/publmat_362a92_15.

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32

Schofield, Aldan. "RING THEORY Volumes I and II." Bulletin of the London Mathematical Society 23, no. 1 (January 1991): 93–94. http://dx.doi.org/10.1112/blms/23.1.93.

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33

Goodearl, K. R. "Book Review: Dimensions of ring theory." Bulletin of the American Mathematical Society 20, no. 1 (January 1, 1989): 107–13. http://dx.doi.org/10.1090/s0273-0979-1989-15718-2.

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34

Ye, Ming-Yong, and Xiu-Min Lin. "Theory of cavity ring-up spectroscopy." Optics Express 25, no. 26 (December 12, 2017): 32395. http://dx.doi.org/10.1364/oe.25.032395.

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35

Foldes, Stephan. "Some ring theory from Jenő Szigeti." Miskolc Mathematical Notes 16, no. 1 (2015): 115. http://dx.doi.org/10.18514/mmn.2015.1726.

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36

Aihara, Jun-ichi. "Graph Theory of Ring-Current Diamagnetism." Bulletin of the Chemical Society of Japan 91, no. 2 (February 15, 2018): 274–303. http://dx.doi.org/10.1246/bcsj.20170318.

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37

Yeh, Pochi. "Theory of unidirectional photorefractive ring oscillators." Journal of the Optical Society of America B 2, no. 12 (December 1, 1985): 1924. http://dx.doi.org/10.1364/josab.2.001924.

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38

Van Oystaeyen, F. "Some applications of graded ring theory." Communications in Algebra 14, no. 8 (January 1986): 1565–96. http://dx.doi.org/10.1080/00927878608823385.

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39

Ypsilantis, T., and J. Seguinot. "Theory of ring imaging Cherenkov counters." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 343, no. 1 (April 1994): 30–51. http://dx.doi.org/10.1016/0168-9002(94)90532-0.

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40

Barnes, Edward O., Ana Fernández-la-Villa, Diego F. Pozo-Ayuso, Mario Castaño-Alvarez, Grace E. M. Lewis, Sara E. C. Dale, Frank Marken, and Richard G. Compton. "Interdigitated ring electrodes: Theory and experiment." Journal of Electroanalytical Chemistry 709 (November 2013): 57–64. http://dx.doi.org/10.1016/j.jelechem.2013.10.009.

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41

Whelan, E. A. "An infinite construction in ring theory." Glasgow Mathematical Journal 30, no. 3 (September 1988): 349–57. http://dx.doi.org/10.1017/s001708950000745x.

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In this note we describe a class of functors on the category of associative rings with unity (hereafter “rings”) and of ring homomorphisms which, loosely speaking, ‘preserve the properties’ of two-sided ideals, but can be chosen to be arbitrarily ‘bad’ for one-sided properties of rings.
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42

Whelan, E. A. "An Infinite Construction in Ring Theory." Glasgow Mathematical Journal 33, no. 1 (January 1991): 121–23. http://dx.doi.org/10.1017/s0017089500008119.

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1. Point (3) of the main theorem of our paper [3, Theorem 1.1] is incorrect: this note corrects the main and consequential errors, and shows that (after minor adjustments) almost all the other results of [3], including the remaining seven points of Theorem 1.1, remain correct.2. The theme of [3] was a family of functors G,(–), defined on the category of rings with unity for each cardinal t. For t = 0, 1, the results of [3] are unchanged, but, for 2≤t<∞, major, and, for t infinite, less major, corrections are necessary; we therefore assume 2≤t. Terminology and notation are standard or as in [3], and I would like to thank A. W. Chatters and an anonymous referee for comments which prompted this correction.
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43

Lizasoain, I., and G. Ochoa. "Clifford theory on the Burnside ring." Archiv der Mathematik 67, no. 3 (September 1996): 183–91. http://dx.doi.org/10.1007/bf01195233.

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44

Kozhukhov, I. B. "Techniques of semigroup ring theory: Artinian, perfect, and semiprimary semigroup rings." Journal of Mathematical Sciences 97, no. 6 (December 1999): 4527–37. http://dx.doi.org/10.1007/bf02364729.

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45

Berry, M. V., M. R. Jeffrey, and J. G. Lunney. "Conical diffraction: observations and theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2070 (February 8, 2006): 1629–42. http://dx.doi.org/10.1098/rspa.2006.1680.

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Conical refraction was produced by a transparent biaxial crystal of KGd(WO 4 ) 2 illuminated by a laser beam. The ring patterns at different distances from the crystal were magnified and projected onto a screen, giving rings whose diameter was 265 mm. Comparison with theory revealed all predicted geometrical and diffraction features: close to the crystal, there are two bright rings of internal conical refraction, separated by the Poggendorff dark ring; secondary diffraction rings decorate the inner bright ring; as the distance from the crystal increases, the inner bright ring condenses onto an axial spot surrounded by diffraction rings. The scales of these features were measured and agreed well with paraxial theory; this involves a single dimensionless parameter ρ 0 , defined as the radius of the rings emerging from the crystal divided by the width of the incident beam. The different features emerge clearly in the asymptotic limit ρ 0 ≫1; in these experiments, ρ 0 =60.
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46

Zhang, Yanbing, Ting Mei, and Dao Hua Zhang. "Temporal coupled-mode theory of ring–bus–ring Mach–Zehnder interferometer." Applied Optics 51, no. 4 (January 27, 2012): 504. http://dx.doi.org/10.1364/ao.51.000504.

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47

LIDOV, DEBORA. "RING." Yale Review 107, no. 3 (2019): 95–96. http://dx.doi.org/10.1353/tyr.2019.0006.

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48

LIDOV, DEBORA. "RING." Yale Review 107, no. 3 (July 2019): 95–96. http://dx.doi.org/10.1111/yrev.13531.

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49

Martinez, J. "The maximal ring of quotientf-ring." Algebra Universalis 33, no. 3 (September 1995): 355–69. http://dx.doi.org/10.1007/bf01190704.

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50

Schenzel, Peter. "Descent from the form ring and buchsbaum rings." Communications in Algebra 24, no. 10 (January 1996): 3283–91. http://dx.doi.org/10.1080/00927879608825750.

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