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Article
Deductive Varieties of Modules and Universal Algebras
Transactions of the American Mathematical Society
  • Leslie Hogben, Iowa State University
  • Clifford Bergman, Iowa State University
Document Type
Article
Disciplines
Publication Date
5-1-1985
Abstract

A variety of universal algebras is called deductive if every subquasivariety is a variety. The following results are obtained: (1) The variety of modules of an Artinian ring is deductive if and only if the ring is the direct sum of matrix rings over local rings, in which the maximal ideal is principal as a left and right ideal. (2) A directly representable variety of finite type is deductive if an only if either (i) it is equationally complete, or (ii) every algebra has an idempotent element, and a ring constructed from the variety is of the form (1) above.

Comments

First published in Transactions of the American Mathematical Society in volume 289, number 1, 1985, published by the American Mathematical Society. Posted with permission.

Copyright Owner
American Mathematical Society
Language
en
Date Available
2015-02-03
File Format
application/pdf
Citation Information
Leslie Hogben and Clifford Bergman. "Deductive Varieties of Modules and Universal Algebras" Transactions of the American Mathematical Society Vol. 289 Iss. 1 (1985) p. 303 - 320
Available at: http://works.bepress.com/clifford_bergman/1/