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1

Cohn, P. M. Algebraic Numbers and Algebraic Functions. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-3444-4.

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2

Bosch, Siegfried. Algebraic Geometry and Commutative Algebra. London: Springer London, 2013.

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3

Bliss, Gilbert Ames. Algebraic functions. Mineola, N.Y: Dover Publications, 2004.

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4

Vostokov, Sergei, and Yuri Zarhin, eds. Algebraic Number Theory and Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/300.

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5

Popov, Vladimir L., ed. Algebraic Transformation Groups and Algebraic Varieties. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05652-3.

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6

Goerss, P. G., and J. F. Jardine, eds. Algebraic K-Theory and Algebraic Topology. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0695-7.

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7

1950-, Shokurov Vyacheslav V., ed. Algebraic curves, algebraic manifolds, and schemes. Berlin: Springer, 1998.

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8

Benedetti, R. Real algebraic and semi-algebraic sets. Paris: Hermann, 1990.

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9

Gregory, Goerss Paul, Jardine J. F. 1951-, and NATO Advanced Study Institute, eds. Algebraic K-theory and algebraic topology. Dordrecht: Kluwer Academic, 1994.

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10

A, Martsinkovsky, Todorov G, Auslander Maurice, and Maurice Auslander Memorial Conference (1995 : Brandeis University), eds. Representation theory and algebraic geometry. Cambridge, UK: Cambridge University Press, 1997.

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11

Kulikov, Viktor S. Algebraic Geometry III: Complex Algebraic Varieties Algebraic Curves and Their Jacobians. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.

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12

Kempf, George. Algebraic varieties. Cambridge: Cambridge University Press, 1993.

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13

Munerman, Viktor, Vadim Borisov, and Aleksandra Kononova. Mass data processing. Algebraic models and methods. ru: INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/1906037.

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The monograph is devoted to mathematical and algorithmic support of mass data processing based on algebraic models. One of the most common classes of mass processing is considered - processing of highly active structured data. The construction of algebraic models of data and calculations and methods of proving their correspondence are analyzed. Three algebraic systems are studied, which can be used both as data models and as models of calculations. The algebraic and axiomatic methods of proving the correspondence of these models are investigated. A proof of their correspondence is given: homomorphism and isomorphism. The problem of optimizing the processes of mass processing of data presented in the form of algebraic expressions in the proposed algebra models is raised. The algorithms of synthesis and optimization of calculation of these expressions, the method of symmetric horizontal data distribution providing parallel implementation of calculation of algebraic expressions and generalization of the block algorithm of parallel matrix multiplication for the case of multiplication of multidimensional matrices are described in detail. Architectures of software and hardware complexes for effective parallel implementation of operations in the considered algebra models are proposed. A number of real-world examples illustrating the application of the proposed methods are given. For students, postgraduates and teachers of technical and physical-mathematical universities and faculties.
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14

Kunz, Ernst. Introduction to Commutative Algebra and Algebraic Geometry. New York, NY: Springer New York, 2013.

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15

Dickson, Leonard E. Algebraic theories. Mineola, N.Y: Dover Publications, 2004.

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16

Mahowald, Mark, and Stewart Priddy, eds. Algebraic Topology. Providence, Rhode Island: American Mathematical Society, 1989. http://dx.doi.org/10.1090/conm/096.

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17

Tschinkel, Yuri, ed. Algebraic groups. Göttingen: Göttingen University Press, 2007. http://dx.doi.org/10.17875/gup2007-57.

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18

Lefschetz, Solomon. Algebraic geometry. Mineola, N.Y: Dover Publications, 2005.

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19

Bray, Clark, Adrian Butscher, and Simon Rubinstein-Salzedo. Algebraic Topology. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70608-1.

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20

Poulakis, Dimitrios, and George Rahonis, eds. Algebraic Informatics. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19685-0.

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21

Stanley, Richard P. Algebraic Combinatorics. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77173-1.

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22

Gindikin, S. G. Algebraic Logic. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-1877-5.

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23

Anai, Hirokazu, Katsuhisa Horimoto, and Temur Kutsia, eds. Algebraic Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-73433-8.

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24

Zariski, Oscar. Algebraic Surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61991-5.

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25

Maletti, Andreas, ed. Algebraic Informatics. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23021-4.

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26

Harris, Joe. Algebraic Geometry. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2189-8.

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27

Stanley, Richard P. Algebraic Combinatorics. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6998-8.

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28

Carlsson, Gunnar, Ralph Cohen, Haynes Miller, and Douglas Ravenel, eds. Algebraic Topology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085212.

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29

Miller, Haynes R., and Douglas C. Ravenel, eds. Algebraic Topology. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078737.

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30

Sommese, Andrew John, Aldo Biancofiore, and Elvira Laura Livorni, eds. Algebraic Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083328.

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31

Cohen, Gérard, Antoine Lobstein, Gilles Zémor, and Simon Litsyn, eds. Algebraic Coding. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0034333.

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32

Abramovich, D., A. Bertram, L. Katzarkov, R. Pandharipande, and M. Thaddeus, eds. Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/pspum/080.1.

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33

Abramovich, D., A. Bertram, L. Katzarkov, R. Pandharipande, and M. Thaddeus, eds. Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/pspum/080.2.

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34

Keum, JongHae, and Shigeyuki Kondō, eds. Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/conm/422.

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35

Przeworska-Rolewicz, Danuta. Algebraic Analysis. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-1427-8.

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36

Muntean, Traian, Dimitrios Poulakis, and Robert Rolland, eds. Algebraic Informatics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-40663-8.

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37

Fløystad, Gunnar, ed. Algebraic Combinatorics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-68376-6.

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38

Bard, Gregory V. Algebraic Cryptanalysis. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-88757-9.

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39

Nguyễn, H. V. Hưng, and Lionel Schwartz, eds. Algebraic Topology. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69434-4.

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40

Cohen, G., S. Litsyn, A. Lobstein, and G. Zémor, eds. Algebraic Coding. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57843-9.

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41

Deo, Satya. Algebraic Topology. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-13-2.

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42

Kempf, George R. Algebraic Structures. Wiesbaden: Vieweg+Teubner Verlag, 1995. http://dx.doi.org/10.1007/978-3-322-80278-1.

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43

Fulton, William. Algebraic Topology. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4180-5.

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44

Deo, Satya. Algebraic Topology. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8734-9.

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45

Winkler, Franz, ed. Algebraic Informatics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21493-6.

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46

Lloris Ruiz, Antonio, Encarnación Castillo Morales, Luis Parrilla Roure, and Antonio García Ríos. Algebraic Circuits. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54649-5.

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47

Bozapalidis, Symeon, and George Rahonis, eds. Algebraic Informatics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03564-7.

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48

Horimoto, Katsuhisa, Georg Regensburger, Markus Rosenkranz, and Hiroshi Yoshida, eds. Algebraic Biology. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85101-1.

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49

Loday, Jean-Louis, and Bruno Vallette. Algebraic Operads. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30362-3.

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50

Kurke, H., and J. H. M. Steenbrink, eds. Algebraic Geometry. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0685-3.

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