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| Paper IPM / M / 92 |
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| Abstract: | |||||
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Let I be an ideal of the commutative ring R and let
\scrptCR denote the category of R-modules and
\scrptCN (resp. \scrptCA) be the
subcategory of Noetherian (resp. Artinian) R-modules. Let N
denote a Noetherian R-module and N′ be a submodule of N. For
a linear exact covariant (resp. contravriant) functor
T:\scrptCN→ \scrptCR,
AssR(T(N)) (resp. AttR(T(N))) is determined
and as a consequence several results concerning asymptotic prime
ideals are deduced. For example, it is shown that both sequences
of sets AssR([(T(N))/(InT(N′))]) and
AssR([(InT(N))/(InT(N′))]) (resp.
AttR(T(N/N′):T(N)In) and
AttR(T(N/N′):T(N)In/0:T(N)In)) are eventually
constant for large n. Also, the dual results are shown to be
true for a linear exact functor T:\scrptC
A→ \scrptCR.
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