On rings for which finitely generated ideals have only finitely many components

2006/01/23 by Thomas Marley, Marley, Thomas
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13B24

paper · pdf · doi:10.48550/arxiv.math/0601566

4 pages

arxiv created 2006/01/23 · arxiv updated 2009/12/01

Abstract

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over R as well as to R-algebras which are finitely presented as R-modules.

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