Radical factorization in finitary ideal systems

2019/03/21 by Olberding, Bruce, Reinhart, Andreas · 1 citation
#13A15 #13F05 #20M12 #20M13 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.09237

Abstract

In this paper we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dedekind r-SP-monoids and provide specific descriptions of t-almost Dedekind t-SP-monoids and w-SP-monoids. We show that a monoid is a w-SP-monoid if and only if the radical of every nontrivial principal ideal is t-invertible. We characterize when the monoid ring is a w-SP-domain and describe when the *-Nagata ring is an SP-domain for a star operation * of finite type.

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• On the arithmetic of polynomial ideals

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