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All rings considered here are commutative rings with identity and all modules considered here are unital left modules. A submodule N of an R-module M is said to be extended to M if $N=aM$ for some ideal a of R and it is said to be fully invariant if ${\varphi}(L){\subseteq}L$ for every ${\varphi}{\in}End(M)$. An R-module M is called a [resp., fully invariant] multiplication module if every [resp., fully invariant] submodule is extended to M. The class of fully invariant multiplication modules is bigger than the class of multiplication modules. We deal with prime submodules and associated prime submodules of fully invariant multiplication modules. In particular, when M is a nonzero faithful multiplication module over a Noetherian ring, we characterize the zero-divisors of M in terms of the associated prime submodules, and we show that the set Aps(M) of associated prime submodules of M determines the set $Zdv_M(M)$ of zero-dvisors of M and the support Supp(M) of M.
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참고문헌 (17)
참고문헌 신청
Reza Ameri / 2003 / On the prime submodules of multiplication modules / Int. J. Math. Math. Sci (27):1715~1724
M. F. Atiyah / 1969 / Introduction to commutative algebra / Addison-Wesley Publishing Co.
Kamran Divaani-Aazar / 2005 / Associated prime sub- modules of finitely generated modules / Comm. Algebra 33(11):4259~4266
David Eisenbud / 1995 / Commutative algebra, Graduate Texts in Mathematics, vol. 150 / Springer-Verlag
Zeinab Abd El-Bast / 1988 / Multiplication modules / Comm. Al- gebra 16(4):755~779
M. F. Atiyah / 1969 / Introduction to commutative algebra / Addison-Wesley Publishing Co.
Kamran Divaani-Aazar / 2005 / Associated prime sub- modules of finitely generated modules / Comm. Algebra 33(11):4259~4266
David Eisenbud / 1995 / Commutative algebra, Graduate Texts in Mathematics, vol. 150 / Springer-Verlag
Zeinab Abd El-Bast / 1988 / Multiplication modules / Comm. Al- gebra 16(4):755~779
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