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On rings all of whose factor rings are integral domains

Published online by Cambridge University Press:  09 April 2009

Yasuyuki Hirano
Yasuyuki Hirano
Affiliation:
Okayama University, Okayama, 700, Japan
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Abstract

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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

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