Star-reductions of ideals and Prufer v-multiplication domains

2016/02/23 by Evan Houston, E. Houston, Houston, E. +4
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13A15 #msc:13A18 #msc:13C20 #msc:13F05 #msc:13G05

paper · pdf · doi:10.48550/arxiv.1602.07035

9 pages. Journal of Commutative Algebra 2016

arxiv created 2016/02/23 · arxiv updated 2016/02/24

Abstract

Let R be a commutative ring and I an ideal of R. A sub-ideal J of I is a reduction of I if JIⁿ = Iⁿ+1 for some positive integer n. The ring R has the (finite) basic ideal property if (finitely generated) ideals of R do not have proper reductions. Hays characterized (one-dimensional) Prufer domains as domains with the finite basic ideal property (basic ideal property). We extend Hays' results to Prufer v-multiplication domains by replacing "basic" with "w-basic," where w is a particular star operation. We also investigate relations among star-basic properties for certain star operations.

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