J Austral Math Soc Ser A 55 pp325--333, 1993.

On Rings all of Whose Factor Rings are Integral Domains

Yasuyuki Hirano

Abstract

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.

1991 AMS Subject Classification: primary 16A45; secondary 16A02, 16A48

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Authors

Yasuyuki Hirano

Okayama University, Okayama, 700, Japan.