McCoy modules and related modules over commutative rings. Issue 6 (3rd June 2017) - Anderson, D. D.; Chun, Sangmin
ABSTRACT: Let M be a left R -module. Then M is a McCoy (resp., dual McCoy) module if for nonzero f ( X )∈ R [ X ] and m ( X )∈ M [ X ], 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.