Normal Domains with Monomial Presentations
نویسندگان
چکیده
Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . , Xn | R〉, where R is a set of monomial relations in the generators X1, . . . , Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1, . . . , Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relations. Also the class group of such algebras A is calculated. Mathematics Subject Classification 2000: primary 16S36, 13B22; secondary 14M25, 16H05, 13C20, 20M14 keywords: normal domain, class group, finitely presented algebra, semigroup algebra, commutative semigroup, normal semigroup
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Integrally closed domains with monomial presentations
Let A be a finitely generated commutative algebra over a field K with a presentation A = K〈X1, . . . ,Xn | R〉, where R is a set of monomial relations in the generators X1, . . . ,Xn. Necessary and sufficient conditions are found for A to be an integrally closed domain provided that the presentation involves at most two relations. The class group of such algebras A is calculated. Examples are gi...
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ورودعنوان ژورنال:
- IJAC
دوره 19 شماره
صفحات -
تاریخ انتشار 2009