A realization theorem for almost Dedekind domains

2024/05/07 by Rago, Balint, Spirito, Dario · 1 citation
#13A15 #13F05 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.04512

Abstract

An integral domain D is called an SP-domain if every ideal is a product of radical ideals. Such domains are always almost Dedekind domains, but not every almost Dedekind domain is an SP-domain. The SP-rank of D provides a natural measure of the deviation of D from being an SP-domain. In the present paper we show that every ordinal number α can be realized as the SP-rank of an almost Dedekind domain.

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