Relative projectivity and related results
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 419-426
Published online September 1, 2004
H. Ansari-Toroghy
Guilan University
Abstract : Let $R$ be a commutative Noetherian ring and let $M$ be an Artinian $R$-module. Let $M'' \subseteq M'$ be submodules of $M$. Suppose $F$ is an $R$-module which is projective relative to $M$. Then it is shown that $$ Att_R(Hom_A(F, M'):_ {Hom_A(F, M)} I^n), \\\ n \in N $$ and $$\aligned & Att_R(Hom_A(F, M'):_ {Hom_A(F, M)} I^n\\ & / Hom_A(F, M''):_ {Hom_A(F, M)} I^n), n \in N \endaligned $$ are ultimately constant.
Keywords : associated primes, relative projectivity, attached primes
MSC numbers : 1.30E+06
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