1981
DOI: 10.1007/bf01849617
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On finitely generated projective ideals in commutative rings

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Cited by 9 publications
(8 citation statements)
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“…Now we give conditions under which a semi-multiplication module becomes projective (compare with the relation between multiplication modules and projective modules [7]). = (al,...,an).…”
Section: W 2 Basic Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Now we give conditions under which a semi-multiplication module becomes projective (compare with the relation between multiplication modules and projective modules [7]). = (al,...,an).…”
Section: W 2 Basic Resultsmentioning
confidence: 99%
“…Now let X = (zl,...,zn) E U j', hence ~oi(~_~aizi) = 0, this implies that Cz t = 0. Consequently M is projective [4]. 9…”
Section: W 2 Basic Resultsmentioning
confidence: 99%
“…. ln), then it can be checked easily t h a t V t --M t V t and V ± ----ann (Mr); and it follows from [11], [6] t h a t P* is projective. Using the same argument, one can show t h a t P** is projective.…”
Section: ~ L(aj) ~ Li(at) X I = L(aj) 1 I a Sx I : L(aj) Lj(x)mentioning
confidence: 99%
“…Multiplication modules have received a lot of attention in recent years (see, for example, [1], [3]- [6], [8], [9]). W. W. Smith [9,Theorem 1] proved that any projective ideal of R is a multiplication R-module.…”
mentioning
confidence: 99%
“…On the other hand, it is well known that a free module is a multiplication module if and only if it has rank 1 (see, for example, [3, Lemma 2.1]). Naoum [5,Theorem 4.1] proved that a finitely generated module M is a multiplication module whose annihilator is generated by an idempotent in R if and only if M is a projective module whose endomorphism ring is commutative (see also [6,Theorem 2.1] and [8,Theorem 11]). In this note we investigate further the relationship between multiplication modules and projective modules.…”
mentioning
confidence: 99%