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- W149299900 abstract "In the first section, we introduce the notion of an h-local maximal ideal as a maximal ideal M of a domain R such that $$Theta (M){R}_{M} = K$$ (the quotient field of R). The second section deals with independent pairs of overrings of a domain R. In the case R can be realized as the intersection of a pair of independent overrings, we show that R shares various factorization properties with these overrings. For example, R has weak factorization if and only if both overrings have weak factorization. The third section introduces Jaffard families and Matlis partitions. Just as domains of Dedekind type are the same as h-local domains, a domain R can be realized as an intersection of the domains of a Jaffard family if and only if its set of maximal ideals can be partitioned into a Matlis partition (definitions below). As in the second section, if $$R ={ bigcap nolimits }_{alpha in mathcal{A}}{S}_{alpha }$$ where $${{S{}_{alpha }}}_{alpha in mathcal{A}}$$ is a Jaffard family, then R satisfies a particular factoring property if and only if each S α satisfies the same factoring property. The last section is devoted to constructing examples using various Jaffard families." @default.
- W149299900 created "2016-06-24" @default.
- W149299900 creator A5011853258 @default.
- W149299900 creator A5014298843 @default.
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- W149299900 date "2012-01-01" @default.
- W149299900 modified "2023-09-23" @default.
- W149299900 title "Factorization and Intersections of Overrings" @default.
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- W149299900 doi "https://doi.org/10.1007/978-3-642-31712-5_6" @default.
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