McCoy modules and related modules over commutative rings |
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| Authors: | D D Anderson |
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| Institution: | Department of Mathematics, The University of Iowa, Iowa City, Iowa, USA |
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| Abstract: | Let M be a left R-module. Then M is a McCoy (resp., dual McCoy) module if for nonzero f(X)∈RX] and m(X)∈MX], f(X)m(X) = 0 implies there exists a nonzero r∈R (resp., m∈M) with rm(X) = 0 (resp., f(X)m = 0). We show that for R commutative every R-module is dual McCoy, but give an example of a non-McCoy module. A number of other results concerning (dual) McCoy modules as well as arithmetical, Gaussian, and Armendariz modules are given. |
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| Keywords: | Arithmetical module Armendariz module dual McCoy module Gaussian module McCoy module |
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