Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T23:13:56.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Special Principal Ideal Rings and Absolute Subretracts

Published online by Cambridge University Press:  20 November 2018

Eric Jespers
Eric Jespers*
Affiliation:
Memorial University of Newfoundland, St. John's, Newfoundland A1C 5S7
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A ring R is said to be an absolute subretract if for any ring S in the variety generated by R and for any ring monomorphism f from R into S, there exists a ring morphism g from S to R such that gf is the identity mapping. This concept, introduced by Gardner and Stewart, is a ring theoretic version of an injective notion in certain varieties investigated by Davey and Kovacs.

Also recall that a special principal ideal ring is a local principal ring with nonzero nilpotent maximal ideal. In this paper (finite) special principal ideal rings that are absolute subretracts are studied.

Keywords

16A5208B30absolute subretractsspecial principal ideal ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 364 - 367
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups. Vol. I, American Mathematical Society, Providence, Rhode Island, 1961.Google Scholar
2. Decruyenaere, F., Jespers, E., Wauters, P., On commutative principal ideal semigroup rings, Semigroup Forum, to appear.Google Scholar
3. Gardner, B. J., Stewart, P. N., Injective and weakly injective rings , Canad. Math. Bull. (4)31(1988), 487–494.Google Scholar
4. Gilmer, R., Commutative semigroup rings. The Univ. of Chicago Press, Chicago and London, 1984.Google Scholar
5. Procesi, C., Rings with polynomial identities. Marcel Dekker, New York, 1973.Google Scholar