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- W2044202578 abstract "PROOF. Let P be a proper prime ideal of R so S = R/P is an integral domain over which every nonzero module has a maximal submodule. Let sQ be a nonzero, injective S-module. Then sQ has a simple epimorphic image, say S/M where M is a maximal ideal of S. If mEM and m#0, then, being the quotient of an injective module, S/M is divisible, and there is an sES with m(s+M) =ms+M= 1+M. Hence 1 CM, a contradiction. Thus M= 0, and S is a field. If RM is an R-module, then RM is R-projective if for each epimorphism a: RR--RC and each homomorphism r: RM-*RC, there is a homomorphism T:RM-*RR such that rT=r. We call a ring R a test module for projectivity if every R-projective module is projective." @default.
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- W2044202578 date "1966-06-01" @default.
- W2044202578 modified "2023-09-28" @default.
- W2044202578 title "Commutative, noetherian rings over which every module has a maximal submodule" @default.
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