Document Type

Article

Publication Date

5-1985

Journal or Book Title

Transactions of the American Mathematical Society

Volume

289

Issue

1

First Page

303

Last Page

320

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

File Format

application/pdf

Included in

Algebra Commons

Share

COinS