No CrossRef data available.
Article contents
On rings all of whose factor rings are integral domains
Published online by Cambridge University Press: 09 April 2009
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 called a (proper) quotient no-zero-divisor ring if every (proper) nonzero factor ring of R has no zero-divisors. A characterization of a quotient no-zero-divisor ring is given. Using it, the additive groups of quotient no-zero-divisor rings are determined. In addition, for an arbitrary positive integer n, a quotient no-zero-divisor ring with exactly n proper ideals is constructed. Finally, proper quotient no-zero-divisor rings and their additive groups are classified.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 325 - 333
- Copyright
- Copyright © Australian Mathematical Society 1993
References
[1]Feigeistock, S., Additive groups of rings, vol. II, Research Notes in Mathematics 169 (Pitman, Boston, 1988).Google Scholar
[3]Herstein, I. N., Rings with involution (University of Chicago Press, Chicago, 1976).Google Scholar
[4]Jategaonkar, V. A., ‘A multiplicative analog of the Weyl algebra’, Comm. Algebra 12 (1984), 1669–1688.CrossRefGoogle Scholar
[6]Rowen, L. H., Polynomial identities in ring theory (Academic Press, New York, 1980).Google Scholar
You have
Access