대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
  • /
  • Pages.251-253
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  • 2025
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A CHARACTERIZATION OF FACTORIAL RINGS

  • Kui Hu (College of Science Southwest University of Science and Technology) ;
  • De Chuan Zhou (College of Science Southwest University of Science and Technology)
  • 투고 : 2024.03.11
  • 심사 : 2024.07.24
  • 발행 : 2025.01.31
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⟨ 이전 논문 다음 논문 ⟩

초록

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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과제정보

This research was supported by National Natural Science Foundation of China (12101515).

참고문헌

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