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- W177674245 abstract "AbstractWe investigate the relationship between projective modules and idempotent ideals for group rings, polynomial rings and more general rings, giving a survey of known results, proving some new results and raising a number of questions. In particular, it is proved that if R is any ring, X a projective right R-module and A an ideal of R such that the R-module X/XA can be generated by a set of elements of cardinality ℵ, for some infinite cardinal ℵ, then X/XB can be generated by a set of elements of cardinality ℵ, where B is the unique maximal idempotent ideal of R contained in A. A recurring theme is that of “intersection theorems” which give information about intersections of powers of ideals of the ring.Mathematics Subject Classification (2000)Primary: 16D2516D40Secondary: 16D3016P4016S3016S3416S36KeywordsProjective moduleidempotent idealNoetherian ringsemiprime ringgroup ringpolynomial ring" @default.
- W177674245 created "2016-06-24" @default.
- W177674245 creator A5012385241 @default.
- W177674245 date "2010-01-01" @default.
- W177674245 modified "2023-09-25" @default.
- W177674245 title "Projective Modules, Idempotent Ideals and Intersection Theorems" @default.
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- W177674245 doi "https://doi.org/10.1007/978-3-0346-0286-0_20" @default.
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