국가지식-학술정보
A CHARACTERIZATION OF FACTORIAL RINGS
A CHARACTERIZATION OF FACTORIAL RINGS
- 대한수학회
- Bulletin of the Korean Mathematical Society
- Vol.62No.1
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2025.01251 - 253 (3 pages)
- 0
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Let R be a commutative ring. It is proved in this note that if every (regular) prime w-ideal of R is principal, then every (regular) w-ideal of R is also principal. It is also proved that if every regularly principal ideal I (regular elements in I are contained in a principal ideal which is generated by a regular element in I) of R is principal, for example, zero-divisors in R are nilpotent, then R is a factorial ring if and only if every regular w-ideal of R is principal.
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