A look at the prime and semiprime operations of one-dimensional domains - Mathematics > Commutative AlgebraReport as inadecuate




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Abstract: We continue the analysis of prime and semiprime operations overone-dimensional domains started in \cite{Va}. We first show that there are nobounded semiprime operations on the set of fractional ideals of aone-dimensional domain. We then prove the only prime operation is the identityon the set of ideals in semigroup rings where the ideals are minimallygenerated by two or fewer elements. This is not likely the case in semigrouprings with ideals of three or more generators since we are able to exhibit thatthere is a non-identity prime operations on the set of ideals of$kt^3,t^4,t^5$.



Author: Janet C. Vassilev

Source: https://arxiv.org/







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