This article is cited in 8 papers

Geometric scales for varieties of algebras and quasi-identities

A. G. Pinus

Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: We introduce a preorder for universal algebras with respect to their geometries. This naturally leads to the notion of the geometric scale for a variety of algebras. We investigate connections between the introduced relation and infinite quasi-identities that hold in algebras, as well as other properties of the relation and the scale.

Key words: universal algebra, algebraic set, geometrically equivalent algebras, quasi-identities.

UDC: 512.56

Received: 26.11.2008

 English version: Siberian Advances in Mathematics, 2010, 20:3, 217–222

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