Content Algebras Over Commutative Rings With Zero-Divisors

Details Content Algebras Over Commutative Rings With Zero-Divisors Content Algebras Over Commutative Rings With Zero-Divisors

2008-07-11

arxiv.org/abs/0807.1835v3

Mathematics

Commutative Algebra

14 pages (Edited and improved, some new results added)

Scientific paper

Let $M$ be an $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{is an ideal of} R \text{and} x \in IM \rbrace $. $M$ 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.

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