2013/12/28 by Christopher Park Mooney, Mooney, Christopher Park
Mathematics · #13A05 #13E99 #13F15 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A05 #msc:13E99 #msc:13F15
paper · pdf · doi:10.48550/arxiv.1312.7400
14 pages, to appear Houston Journal of Mathematics
arxiv created 2013/12/28 · arxiv updated 2013/12/31
Much work has been done on generalized factorization techniques in integral domains, namely τ-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 τ-factorization to commutative rings that need not be domains. In addition, we look into particular types of τ 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.