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Journal of Siberian Federal University. Mathematics & Physics, 2013, Volume 6, Issue 4, Pages 521–526 (Mi jsfu341)  
This article is cited in 1 scientific paper (total in 1 paper)

Equationally noetherian algebras and chain conditions

Mohammad Shahryari

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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Abstract: In this article, we describe the relation between the properties of being equational noetherian and ascending chain condition on ideals of an arbitrary algebra. We also give a formulation of Hilbert's basis theorem for varieties of algebras and obtain a criterion to investigate it for a given variety.
Keywords: algebraic structures, equations, algebraic set, radical ideal, coordinate algebra, Zariski topology, noetherain algebra, equationally noetherian algebra, pre-variety, variety, free product, $\max$-$n$ group, Hilbert's basis theorem.
Received: 26.09.2013
Received in revised form: 06.10.2013
Accepted: 06.11.2013
Document Type: Article
UDC: 512.5
Language: English
Citation: Mohammad Shahryari, “Equationally noetherian algebras and chain conditions”, J. Sib. Fed. Univ. Math. Phys., 6:4 (2013), 521–526
Citation in format AMSBIB
\Bibitem{Sha13}
\by Mohammad~Shahryari
\paper Equationally noetherian algebras and chain conditions
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 4
\pages 521--526
\mathnet{http://mi.mathnet.ru/jsfu341}
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    • This publication is cited in the following 1 articles:
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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