Content Algebras Over Commutative Rings With Zero-Divisors

Peyman Nasehpour

Content Algebras Over Commutative Rings With Zero-Divisors

Commutative Algebra 2015-09-03 v4 Rings and Algebras

Authors: Peyman Nasehpour

Abstract

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.

Keywords

module theory commutative ring theory ideal theory

Cite

@article{arxiv.0807.1835,
  title  = {Content Algebras Over Commutative Rings With Zero-Divisors},
  author = {Peyman Nasehpour},
  journal= {arXiv preprint arXiv:0807.1835},
  year   = {2015}
}

Comments

15 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

Content Algebras Over Commutative Rings With Zero-Divisors

Abstract

Keywords

Cite

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