B. Plotkin, A. Tsurkov, “Action type geometrical equivalence of representations of groups”, Algebra Discrete Math., 2005, no. 4, 48

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Algebra and Discrete Mathematics, 2005, Issue 4, Pages 48–79 (Mi adm320)

This article is cited in 10 scientific papers (total in 10 papers)

RESEARCH ARTICLE

Action type geometrical equivalence of representations of groups

B. Plotkin^a, A. Tsurkov^b

^a Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, 91904, Israel
^b Department of Mathematics and Statistics, Bar Ilan University, Ramat Gan, 52900, Israel

Full-text PDF (356 kB) Citations (10)

Abstract: In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over

K F_{2}

$KF_{2}$ where

F_{2}

$F_{2}$ is a free group with

2

$2$ generators (compare with [Ca] where a continuum of non isomorphic simple

2

$2$ -generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9).

Received: 30.10.2005
Revised: 15.12.2005

Bibliographic databases:

Document Type: Article

Language: English

Citation: B. Plotkin, A. Tsurkov, “Action type geometrical equivalence of representations of groups”, Algebra Discrete Math., 2005, no. 4, 48–79

Citation in format AMSBIB

\Bibitem{PloTsu05}

\by B.~Plotkin, A.~Tsurkov

\paper Action type geometrical equivalence of representations of groups

\jour Algebra Discrete Math.

\yr 2005

\issue 4

\pages 48--79

\mathnet{http://mi.mathnet.ru/adm320}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2237702}

\zmath{https://zbmath.org/?q=an:1092.20005}

Linking options:

https://www.mathnet.ru/eng/adm320

https://www.mathnet.ru/eng/adm/y2005/i4/p48

This publication is cited in the following 10 articles:

J. Simões da Silva, A. Tsurkov, “Geometrical equivalence and action type geometrical equivalence of group representations”, Algebra Discrete Math., 30:2 (2020), 273–281
Tsurkov A., “Automorphic Equivalence in the Varieties of Representations of Lie Algebras”, Commun. Algebr., 48:1 (2020), 397–409
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures”, J. Math. Sci., 257:6 (2021), 797–813
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra and Logic, 56:4 (2017), 281–294
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Universal geometrical equivalence of the algebraic structures of common signature”, Siberian Math. J., 58:5 (2017), 801–812
Tsurkov A., “Automorphic Equivalence of Many-Sorted Algebras”, Appl. Categ. Struct., 24:3 (2016), 209–240
Plotkin B., Plotkin E., “Multi-Sorted Logic and Logical Geometry: Some Problems”, Demonstr. Math., 48:4, SI (2015), 578–619
I. Shestakov, A. Tsurkov, “Automorphic equivalence of the representations of Lie algebras”, Algebra Discrete Math., 15:1 (2013), 96–126
E. Aladova, A. A. Gvaramiya, B. I. Plotkin, “Logic in representations of groups”, Algebra and Logic, 51:1 (2012), 1–27
Plotkin B., “Some Results and Problems Related to Universal Algebraic Geometry”, Int. J. Algebr. Comput., 17:5-6 (2007), 1133–1164

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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