McCoy modules and related modules over commutative rings

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.

KEYWORDS:

• Arithmetical module
• Armendariz module
• dual McCoy module
• Gaussian module
• McCoy module

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13C13
• Secondary: 16D80