컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0565 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Algebra / Representation Theory / Lie Theory (SS-02) |
| 영문제목 (Title(Eng.)) |
Some remarks on LCM-stable modules |
| 저자(Author(s)) |
Hwankoo Kim1, Fanggui Wang2 Hoseo University1, Sichuan Normal University2 |
| 초록본문(Abstract) | A torsion-free module $M$ over an integral domain $R$ is said to be LCM-stable over $R$ if $(Ra \cap Rb)M = Ma \cap Mb$ for all $a, b \in R$. We show that if the module $M$ is LCM-stable over a GCD-domain $R$, then the polynomial module $M[X]$ is LCM-stable over $R[X]$; if $R$ is a $w$-coherent locally GCD-domain, then LCM-stability and reflexivity are equivalent for $w$-finite type torsion-free $R$-modules. Finally we introduce the concept of $w$-LCM-stability for modules over a domain. Then we characterize when the module $M$ is $w$-LCM-stable over the domain in terms of localizations and $t$-Nagata modules respectively. Also we characterize Pr\"ufer $v$-multiplication domains and Krull domains in terms of $w$-LCM-stability. |
| 분류기호 (MSC number(s)) |
13A15, 13G05 |
| 키워드(Keyword(s)) | LCM-stable, $w$-LCM-stable, P$v$MD, $w$-module, 2-$w$-module |
| 강연 형태 (Language of Session (Talk)) |
English |