Article
Deductive varieties of modules and universal algebras
Transactions of the American Mathematical Society
Document Type
Article
Disciplines
- Algebra and
- Mathematics
Publication Version
Published Version
Publication Date
5-1-1985
DOI
10.1090/S0002-9947-1985-0779065-X
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.
Copyright Owner
American Mathematical Society
Copyright Date
1985
Language
en
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/leslie-hogben/1/
This article is published as Hogben, Leslie, and Clifford Bergman. "Deductive varieties of modules and universal algebras." Transactions of the American Mathematical Society 289, no. 1 (1985): 303-320. DOI: 10.1090/S0002-9947-1985-0779065-X. Posted with permission.