On P-exchange rings
type: Item
instance of: scholarly article
title: On P-exchange rings
zbMATH Open document ID: 0712.16006
author: Hikoji Kambara
author: Kiyoichi Oshiro
published in: Osaka Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A module M over some ring is said to have the exchange property, if for each direct sum \(X=\oplus_{i\in I}X_ i\) of modules containing M as a direct summand there exists a family \(X_ i'\subset X_ i\), \(i\in I\), such that \(M=\oplus_{i\in I}X_ i'\). There is a number of unsolved questions concerning this property, for instance to determine those rings, over which all projective right modules have the exchange property. The present paper contributes some results to this problem. Among other things it is shown that all projective right modules over a ring R have the exchange property if and only if this holds for all Pierce stalks \(R_ x\) of R (for the definition of \(R_ x\) see [\textit{R. S. Pierce}: Modules over commutative regular rings (Mem. Am. Math. Soc. 70, 1967; Zbl 0152.026)]).
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 4171145
zbMATH Keywords: exchange property
zbMATH Keywords: direct sum
zbMATH Keywords: projective right modules
zbMATH Keywords: Pierce stalks
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171145