컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0241 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-03) Commutative Algebra and Related Topics (SS-03) |
| 발표시간(Time) | 20th-C-10:00 -- 10:20 |
| 영문제목 (Title(Eng.)) |
The $\phi$-weak dimension of strongly $\phi$-pseudo-valuation rings |
| 저자(Author(s)) |
Hwankoo Kim1, Najib Mahdou2, El Houssaine Oubouhou2 Hoseo University1, University S.M. Ben Abdellah Fez2 |
| 초록본문(Abstract) | In this talk, we prove that the $\phi$-weak global dimension of strongly $\phi$-pseudo-valuation rings is 0, 1, 2 or $\infty$. Furthermore, the only possible values of the $\phi$-weak global dimension of a strongly $\phi$-pseudo-valuation ring that is nonnil-coherent are 0, 1, and $\infty$. We then give necessary and sufficient conditions for a strongly $\phi$-pseudo-valuation ring to be nonnil-coherent. As an application, we show that if $R$ is a strongly nonnil-coherent $\phi$-pseudo-valuation ring, then any overring $B$ of $R$ is also a nonnil-coherent $\phi$-pseudo-valuation ring. |
| 분류기호 (MSC number(s)) |
13D05, 13A18, 13C11 |
| 키워드(Keyword(s)) | $\phi$-weak global dimension, $\phi$-pseudo-valuation rings, Pseudo-valuation domains, $\phi$-CR rings, Strongly $\phi$-rings |
| 강연 형태 (Language of Session (Talk)) |
Korean |