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2016 $\tau $-Regular factorization in commutative rings with zero-divisors
Christopher Park Mooney
Rocky Mountain J. Math. 46(4): 1309-1349 (2016). DOI: 10.1216/RMJ-2016-46-4-1309


Recently there has been a flurry of research on generalized factorization techniques in both integral domains and rings with zero-divisors, namely, $\tau $-factorization. There are several ways that authors have studied factorization in rings with zero-divisors. This paper focuses on the method of regular factorizations introduced by Anderson and Valdes-Leon. We investigate how one can extend the notion of $\tau $-factorization to commutative rings with zero-divisors by using the regular factorization approach. The study of regular factorization is particularly effective because the distinct notions of associate and irreducible coincide for regular elements. We also note that the popular U-factorization developed by Fletcher also coincides since every regular divisor is essential. This will greatly simplify many of the cumbersome finite factorization definitions that exist in the literature when studying factorization in rings with zero-divisors.


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Christopher Park Mooney. "$\tau $-Regular factorization in commutative rings with zero-divisors." Rocky Mountain J. Math. 46 (4) 1309 - 1349, 2016.


Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1364.13003
MathSciNet: MR3563184
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1309

Primary: 13A05 , 13E99 , 13F15

Keywords: commutative rings , factorization , regular and U-factorization , zero-divisors

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 4 • 2016
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