Integral Domains in which Every Nonzerot-Locally Principal Ideal ist-Invertible
In: Communications in Algebra, Jg. 41 (2013-10-03), S. 3805-3819
Online
unknown
Zugriff:
Let D be an integral domain, D[X] be the polynomial ring over D, and w be the so-called w-operation on D. We define D to be a w-LPI domain if every nonzero w-locally principal ideal of D is w-invertible. This article presents some properties of w-LPI domains. It is shown that D is a w-LPI domain if and only if D[X] is a w-LPI domain, if and only if D[X] N v is an LPI domain, where N v = {f ∈ D[X] | c(f)−1 = D}. As a corollary, it is also shown that D is a w-LPI domain if and only if each w-locally finitely generated and w-locally free submodule of D n of rank n over D is of w-finite type. We show that if is a finite character intersection of t-linked overrings D α and if each D α is a w-LPI domain, then D is a w-LPI domain.
Titel: |
Integral Domains in which Every Nonzerot-Locally Principal Ideal ist-Invertible
|
---|---|
Autor/in / Beteiligte Person: | Gyu Whan Chang ; Kim, Hwankoo ; Jung Wook Lim |
Link: | |
Zeitschrift: | Communications in Algebra, Jg. 41 (2013-10-03), S. 3805-3819 |
Veröffentlichung: | Informa UK Limited, 2013 |
Medientyp: | unknown |
ISSN: | 1532-4125 (print) ; 0092-7872 (print) |
DOI: | 10.1080/00927872.2012.678022 |
Schlagwort: |
|
Sonstiges: |
|