for commutative rings with identity

Authors:
John Lawrence and Boza Tasic

Journal:
Proc. Amer. Math. Soc. **134** (2006), 943-948

MSC (2000):
Primary 06F05, 68Q99

DOI:
https://doi.org/10.1090/S0002-9939-05-08066-4

Published electronically:
July 25, 2005

MathSciNet review:
2196024

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let , , , , be the usual operators on classes of rings: and for isomorphic and homomorphic images of rings and , , respectively for subrings, direct, and subdirect products of rings. If is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class is known to be the variety generated by the class . Although the class is in general a proper subclass of the class for many familiar varieties . Our goal is to give an example of a class of commutative rings with identity such that . As a consequence we will describe the structure of two partially ordered monoids of operators.

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Additional Information

**John Lawrence**

Affiliation:
University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, Canada N2L 3G1

Email:
jwlawren@math.uwaterloo.ca

**Boza Tasic**

Affiliation:
University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, Canada N2L 3G1

Email:
btasic@math.uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9939-05-08066-4

Keywords:
Class operators,
commutative rings with identity,
partially ordered monoid

Received by editor(s):
November 29, 2001

Received by editor(s) in revised form:
October 28, 2004

Published electronically:
July 25, 2005

Communicated by:
Lance W. Small

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.