Darani, Ahmad Yousefian Notes on annihilator conditions in modules over commutative rings. (English) Zbl 1224.13002 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 18, No. 2, 59-72 (2010). Summary: Let \(M\) be a module over the commutative ring \(R\). In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by \(Z_R(M)\) the set of all zero-divisors of \(R\) on \(M\). \(M\) is said to be strongly coprimal (resp. super coprimal) if for arbitrary \(a,b\in Z_R(M)\) (resp. every finite subset \(F\) of \(Z_R(M)\)) the annihilator of \(\{a,b\}\) (resp. \(F\)) in \(M\) is non-zero. In this paper we give some results on these classes of modules. We also provide a relationship between the families of coprimal, strongly coprimal and super coprimal modules. We prove that if \(M\) is a coprimal module of finite Goldie dimension over a commutative ring, then \(M\) is super coprimal. Finally we show that every proper submodule of a module over a Prüfer domain of finite character can be expressed as a finite intersection of strongly primal submodules. Cited in 9 Documents MSC: 13A05 Divisibility and factorizations in commutative rings 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations Keywords:coprimal module; strongly coprimal module; super coprimal module; McCoy module PDFBibTeX XMLCite \textit{A. Y. Darani}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 18, No. 2, 59--72 (2010; Zbl 1224.13002) Full Text: EuDML