Finitely t-valuative domains
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let D be an integral domain with quotient field K. In [1], the authors called D a finitely valuative domain if, for each 0 neq u in K, there is a saturated chain of rings (formula). They then studied some properties of finitely valuative domains. For example, they showed that the integral closure of a finitely valuative domain is a Pr"ufer domain. In this paper, we introduce the notion of finitely t-valuative domains, which is the t-operation analog of finitely valuative domains, and we then generalize some properties of finitely valuative domains.
Abstract
Let D be an integral domain with quotient field K. In [1], the authors called D a finitely valuative domain if, for each 0 neq u in K, there is a saturated chain of rings (formula). They then studied some properties of finitely valuative domains. For example, they showed that the integral closure of a finitely valuative domain is a Pr"ufer domain. In this paper, we introduce the notion of finitely t-valuative domains, which is the t-operation analog of finitely valuative domains, and we then generalize some properties of finitely valuative domains.
참고문헌 (7)
- P.-J. Cahen, "Finitely valuative domains", J. Algebra Appl, 6, pp.1250112~ (2012)
- Nv, "J. Pure Appl. Algebra", 2005, 293~304
- 장규환, "Overrings of the Kronecker function ring Kr(D, *) of a Prüfer *-multiplication domain D", 대한수학회보, 46(5), pp.1013~1018 (2009), 대한수학회
- G.W. Chang, "Upper to zero in polynomial rings and Prufer-like domains", Comm. Algebra, 37, pp.164~192 (2009)
- M. Fontana, "UMT-domains and domains with Prufer integral closure", Comm. Algebra, 26, pp.1017~1039 (1998)
- E. Houston, "On t-invertibility II", Comm. Algebra, 17, pp.1955~1969 (1989)
- Nv, "J. Algebra", 1989, 151~170