for commutative rings with identity
Authors:
John Lawrence and Boza Tasic
Journal:
Proc. Amer. Math. Soc. 134 (2006), 943948
MSC (2000):
Primary 06F05, 68Q99
Published electronically:
July 25, 2005
MathSciNet review:
2196024
Fulltext PDF Free Access
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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:
http://dx.doi.org/10.1090/S0002993905080664
PII:
S 00029939(05)080664
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.
