A look at the prime and semiprime operations of one-dimensional domains

2009/05/07 by Janet Vassilev, Janet C. Vassilev, Vassilev, Janet C.
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13A15 #msc:13B22 #msc:13C99

paper · pdf · doi:10.48550/arxiv.0905.1117

arxiv created 2009/05/07 · arxiv updated 2009/12/01

Abstract

We continue the analysis of prime and semiprime operations over one-dimensional domains started in \citeVa. We first show that there are no bounded semiprime operations on the set of fractional ideals of a one-dimensional domain. We then prove the only prime operation is the identity on the set of ideals in semigroup rings where the ideals are minimally generated by two or fewer elements. This is not likely the case in semigroup rings with ideals of three or more generators since we are able to exhibit that there is a non-identity prime operations on the set of ideals of k[[t³,t⁴,t⁵]].

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