Content Algebras Over Commutative Rings With Zero-Divisors

Abstract

Let $M$ be an $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x)=\cap \{I:I\text{is an ideal of}R\text{and}x\in IM\}$. $M$ is said to be a content $R$-module if $x\in c(x)M$, for all $x\in M$. $B$ is called a content $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In this article, we prove some new results for content modules and algebras by using ideal theoretic methods.

arXiv comment15 pages. Note: Since the author has cited to this preprint in some of his papers, it was necessary to update and edit it for the convenience of the readers of his papers