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arXiv · 1312.7400

Generalized Factorization in Commutative Rings with Zero-Divisors

Christopher Park Mooney
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Abstract

Much work has been done on generalized factorization techniques in integral domains, namely $\tau$-factorization. There has also been substantial progress made in investigating factorization in commutative rings with zero-divisors. This paper seeks to synthesize work done in these two areas and extend the notion of $\tau$-factorization to commutative rings that need not be domains. In addition, we look into particular types of $\tau$ relations, which are interesting when there are zero-divisors present. We then proceed to classify commutative rings that satisfy the finite factorization properties given in this paper.

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Christopher Park Mooney. 2013-12-28. Generalized Factorization in Commutative Rings with Zero-Divisors. https://arxiv.org/abs/1312.7400

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