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• W2080454501 abstract "Let R be a local one-dimensional domain. We investigate when the class semigroup S ( R ) of R is a Clifford semigroup. We make use of the Archimedean valuation domains which dominate R , as a main tool to study its class semigroup. We prove that if S ( R ) is Clifford, then every element of the integral closure R ̄ of R is quadratic. As a consequence, such an R may be dominated by at most two distinct Archimedean valuation domains, and R ̄ coincides with their intersection. When S ( R ) is Clifford, we find conditions for S ( R ) to be a Boolean semigroup. We derive that R is almost perfect with Boolean class semigroup if, and only if R is stable. We also find results on S ( R ) , through examination of [ V / P : R / M ] and v ( M ) , where V dominates R , and P , M are the respective maximal ideals." @default.
• W2080454501 created "2016-06-24" @default.
• W2080454501 creator A5071863360 @default.
• W2080454501 date "2008-10-01" @default.
• W2080454501 modified "2023-10-16" @default.
• W2080454501 title "The class semigroup of local one-dimensional domains" @default.
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• W2080454501 doi "https://doi.org/10.1016/j.jpaa.2008.03.015" @default.
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