Mohammad Shahryari, “Equationally noetherian algebras and chain conditions”, J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 4,Pages <nobr>521

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Equationally noetherian algebras and chain conditions

Mohammad Shahryari

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

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.

UDC: 512.5

Received: 26.09.2013
Received in revised form: 06.10.2013
Accepted: 06.11.2013

Language: English