Relevant bibliographies by topics / Elementary Type Conjecture

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Elementary Type Conjecture'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Elementary Type Conjecture"

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Keller, Timothy. "Witt groups and the elementary type conjecture." Communications in Algebra 23, no. 1 (January 1995): 277–89. http://dx.doi.org/10.1080/00927879508825221.

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2

Amir, Firana, and Mohammad Faizal Amir. "Action Proof: Analyzing Elementary School Students Informal Proving Stages through Counter-examples." International Journal of Elementary Education 5, no. 2 (August 23, 2021): 401. http://dx.doi.org/10.23887/ijee.v5i3.35089.

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Both female and male elementary school students have difficulty doing action proof by using manipulative objects to provide conjectures and proof of the truth of a mathematical statement. Counter-examples can help elementary school students build informal proof stages to propose conjectures and proof of the truth of a mathematical statement more precisely. This study analyzes the action proof stages through counter-examples stimulation for male and female students in elementary schools. The action proof stage in this study focuses on three stages: proved their primitive conjecture, confronted counter-examples, and re-examined the conjecture and proof. The type of research used is qualitative with a case study approach. The research subjects were two of the 40 fifth-grade students selected purposively. The research instrument used is the task of proof and interview guidelines. Data collection techniques consist of Tasks, documentation, and interviews. The data analysis technique consists of three stages: data reduction, data presentation, and concluding. The analysis results show that at the stage of proving their primitive conjecture, the conjectures made by female and male students through action proofs using manipulative objects are still wrong. At the stage of confronted counter-examples, conjectures and proof made by female and male students showed an improvement. At the stage of re-examining the conjecture and proof, the conjectures and proof by female and male students were comprehensive. It can be concluded that the stages of proof of the actions of female and male students using manipulative objects through stimulation counter-examples indicate an improvement in conjectures and more comprehensive proof.
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Labute, John, Nicole Lemire, Ján Mináč, and John Swallow. "Demuškin groups, Galois modules, and the Elementary Type Conjecture." Journal of Algebra 304, no. 2 (October 2006): 1130–46. http://dx.doi.org/10.1016/j.jalgebra.2005.12.021.

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4

AUINGER, K. "A NEW PROOF OF THE RHODES TYPE II CONJECTURE." International Journal of Algebra and Computation 14, no. 05n06 (October 2004): 551–68. http://dx.doi.org/10.1142/s0218196704001918.

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For a given finite monoid M we explicitly construct a finite group G and a relational morphism τ:M→G such that only elements of the type II construct Mc relate to 1 under τ. This provides an elementary and constructive proof of the type II conjecture of John Rhodes. The underlying idea is also used to modify the proof of Ash's celebrated theorem on inevitable graphs. For any finite monoid M and any finite graph Γ a finite group G is constructed which "spoils" all labelings of Γ over M which are not inevitable.
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Van Der Ploeg, C. E. "On a Converse to the Tscgebotarev density theorem." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 3 (June 1988): 287–93. http://dx.doi.org/10.1017/s1446788700032109.

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AbstractUsing an elementary counting procedure on biquadratic polynomials over Zp it is shown that the probability distribution of odd, unramified rational primes according to decomposition type in a fixed dihedral numberfield is identical to the probility of separable quartic polynomials (mod p) whose roots generate numberfields with normal closure having Galois group isomorphic to D4, as p → ∞. This verifies a conjecture about a converse to the Tschebotarev density theorem. Further evidence in support of this conjecture is provided in quadratic and coubic numberfields.
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Griffeth, Stephen. "Towards a combinatorial representation theory for the rational Cherednik algebra of type G(r, p, n)." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (April 30, 2010): 419–45. http://dx.doi.org/10.1017/s0013091508000904.

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AbstractThis paper aims to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category $\mathcal{O}$ for the rational Cherednik algebra of type G(r, p, n). As a first application, a self-contained and elementary proof of the analogue for the groups G(r, p, n), with r > 1, of Gordon's Theorem (previously Haiman's Conjecture) on the diagonal co-invariant ring is given. No restriction is imposed on p; the result for p ≠ r has been proved by Vale using a technique analogous to Gordon's. Because of the combinatorial application to Haiman's Conjecture, the paper is logically self-contained except for standard facts about complex reflection groups. The main results should be accessible to mathematicians working in algebraic combinatorics who are unfamiliar with the impressive range of ideas used in Gordon's proof of his theorem.
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Zannier, U. "On a theorem of Birch concerning sums of distinct integers taken from certain sequences." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 2 (September 1989): 199–206. http://dx.doi.org/10.1017/s0305004100078014.

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In [1] B. J. Birch, solving in the affirmative a conjecture of Erdὅs, proved the following result:Theorem 1. Let p and q be coprime integers greater than 1. Then every large natural number may be written as a sum of distinct terms of type paqb.In fact Birch pointed out that, with similar arguments, one could obtain a stronger version where the exponent b of q can be bounded in terms of p and q. The proofs were entirely elementary.
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Yu, Yahui, and Jiayuan Hu. "On the generalized Ramanujan-Nagell equation $ x^2+(2k-1)^y = k^z $ with $ k\equiv 3 $ (mod 4)." AIMS Mathematics 6, no. 10 (2021): 10596–601. http://dx.doi.org/10.3934/math.2021615.

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<abstract><p>Let $ k $ be a fixed positive integer with $ k &gt; 1 $. In 2014, N. Terai <sup>[<xref ref-type="bibr" rid="b6">6</xref>]</sup> conjectured that the equation $ x^2+(2k-1)^y = k^z $ has only the positive integer solution $ (x, y, z) = (k-1, 1, 2) $. This is still an unsolved problem as yet. For any positive integer $ n $, let $ Q(n) $ denote the squarefree part of $ n $. In this paper, using some elementary methods, we prove that if $ k\equiv 3 $ (mod 4) and $ Q(k-1)\ge 2.11 $ log $ k $, then the equation has only the positive integer solution $ (x, y, z) = (k-1, 1, 2) $. It can thus be seen that Terai's conjecture is true for almost all positive integers $ k $ with $ k\equiv 3 $(mod 4).</p></abstract>
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9

Fitzgerald, Robert W. "Gorenstein Witt Rings." Canadian Journal of Mathematics 40, no. 5 (October 1, 1988): 1186–202. http://dx.doi.org/10.4153/cjm-1988-050-x.

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Throughout R is a noetherian Witt ring. The basic example is the Witt ring WF of a field F of characteristic not 2 and finite. We study the structure of (noetherian) Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). The underlying motivation is the elementary type conjecture. The Gorenstein Witt rings of elementary type are group ring extensions of Witt rings of local type. We thus wish to compare the two classes of Witt rings: Gorenstein and group ring over local type. We show the two classes enjoy many of the same properties and are, in several cases, equal. However we cannot decide if the two classes are always equal.In the first section we consider formally real Witt rings R (equivalently, dim R = 1). Here the total quotient ring of R is R-injective if and only if R is reduced. Further, R is Gorenstein if and only if R is a group ring over Z. This result appears to be somewhat deep.
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10

Abe, Hiraku, Megumi Harada, Tatsuya Horiguchi, and Mikiya Masuda. "The Cohomology Rings of Regular Nilpotent Hessenberg Varieties in Lie Type A." International Mathematics Research Notices 2019, no. 17 (October 16, 2017): 5316–88. http://dx.doi.org/10.1093/imrn/rnx275.

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AbstractLet $n$ be a fixed positive integer and $h: \{1,2,\ldots,n\} \rightarrow \{1,2,\ldots,n\}$ a Hessenberg function. The main results of this paper are two-fold. First, we give a systematic method, depending in a simple manner on the Hessenberg function $h$, for producing an explicit presentation by generators and relations of the cohomology ring $H^\ast({\mathrm{Hess}}(\mathsf{N},h))$ with ${\mathbb Q}$ coefficients of the corresponding regular nilpotent Hessenberg variety ${\mathrm{Hess}}(\mathsf{N},h)$. Our result generalizes known results in special cases such as the Peterson variety and also allows us to answer a question posed by Mbirika and Tymoczko. Moreover, our list of generators in fact forms a regular sequence, allowing us to use techniques from commutative algebra in our arguments. Our second main result gives an isomorphism between the cohomology ring $H^*({\mathrm{Hess}}(\mathsf{N},h))$ of the regular nilpotent Hessenberg variety and the $\mathfrak{S}_n$-invariant subring $H^*({\mathrm{Hess}}(\mathsf{S},h))^{\mathfrak{S}_n}$ of the cohomology ring of the regular semisimple Hessenberg variety (with respect to the $\mathfrak{S}_n$-action on $H^*({\mathrm{Hess}}(\mathsf{S},h))$ defined by Tymoczko). Our second main result implies that $\mathrm{dim}_{{\mathbb Q}} H^k({\mathrm{Hess}}(\mathsf{N},h)) = \mathrm{dim}_{{\mathbb Q}} H^k({\mathrm{Hess}}(\mathsf{S},h))^{\mathfrak{S}_n}$ for all $k$ and hence partially proves the Shareshian–Wachs conjecture in combinatorics, which is in turn related to the well-known Stanley–Stembridge conjecture. A proof of the full Shareshian–Wachs conjecture was recently given by Brosnan and Chow, and independently by Guay–Paquet, but in our special case, our methods yield a stronger result (i.e., an isomorphism of rings) by more elementary considerations. This article provides detailed proofs of results we recorded previously in a research announcement [2].
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Dissertations / Theses on the topic "Elementary Type Conjecture"

1

QUADRELLI, CLAUDIO. "Cohomology of Absolute Galois Groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/56993.

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The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group. We define a new class of pro-p groups, called Bloch-Kato pro-p group, whose Galois cohomology satisfies the consequences of the Bloch-Kato conjecture. Also we introduce the notion of cyclotomic orientation for a pro-p group. With this approach, we are able to recover new substantial information about the structure of maximal pro-p Galois groups, and in particular on theta-abelian pro-p groups, which represent the "upper bound" of such groups. Also, we study the restricted Lie algebra and the universal envelope induced by the Zassenhaus filtration of a maximal pro-p Galois group, and their relations with Galois cohomology via Koszul duality. Altogether, this thesis provides a rather new approach to maximal pro-p Galois groups, besides new substantial results.
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