Equationally noetherian algebras and chain conditions

Mohammad Shahryari

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 521-526.

Résumé

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.

Détail

Keywords: algebraic set, radical ideal, coordinate algebra, Zariski topology, noetherain algebra, equationally noetherian algebra, pre-variety, variety, free product, Hilbert's basis theorem.
Mots-clés : algebraic structures, equations, $\max$-$n$ group

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