Generalizations of Nagata's theorem. Issue 5 (4th May 2021)

• Record Type: Journal Article
• Authors: Hamed, Ahmed; Maaref, Walid; Khani-Nasab, Omid
• Is Part Of: Communications in algebra. Volume 49:Issue 5(2021)
• Page Start: 2033
• Page End: 2040
• Publication Date: 2021-05-04
• Subjects: S-class group of an integral domain -- Archimedean domain; 13C20 -- 13F05 -- 13A15 -- 13G05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1862138
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let D be an integral domain and S a multiplicative subset of D . According to the study of Hamed and Hizem, the S -class group of D, denoted by S - C l t ( D ), is the group of fractional t -invertible t -ideals of D under the t -multiplication modulo its subgroup of S -principal t -invertible t -ideals of D . In this paper we study the case of isomorphism S - C l t ( D ) ≃ S - C l t ( D T ), where T is a multiplicative subset generated by prime elements of D . In particular we give a new S -version of Nagata's theorem.