McCoy modules and related modules over commutative rings. Issue 6 (3rd June 2017)

• Record Type: Journal Article
• Authors: Anderson, D. D.; Chun, Sangmin
• Is Part Of: Communications in algebra. Volume 45:Issue 6(2017)
• Page Start: 2593
• Page End: 2601
• Publication Date: 2017-06-03
• Subjects: Arithmetical module -- Armendariz module -- dual McCoy module -- Gaussian module -- McCoy module; Primary: 13C13 -- Secondary: 16D80; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1233218
• Languages: English
• ISSNs: 0092-7872

Abstract

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.