Bezout Overrings of a Polynomial Ring D[{Xα}]. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Chang, Gyu Whan
• Is Part Of: Communications in algebra. Volume 44:Issue 8(2016)
• Page Start: 3211
• Page End: 3218
• Publication Date: 2016-08-02
• Subjects: Bezout domain -- e.a.b. star operation -- Polynomial ring -- Prüfer domain; 13A15 -- 13B25 -- 13F05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1065869
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let D be an integral domain with quotient field K, Λ be an index set with |Λ| ≥1, { X α ∣α ∈ Λ} be a set of indeterminates over D, { V λ } be the set of valuation overrings of D, and It is known that R 2 is a Bezout domain. In this article, we show that R 1 is a PID and R is a Bezout domain. We also show that D is a Prüfer domain if and only if R = D [{ X α }] S, if and only if D [{ X α }] S is a Bezout domain, where .