Goto Numbers of a Numerical Semigroup Ring and the Gorensteiness of Associated Graded Rings
نویسنده
چکیده
The Goto number of a parameter ideal Q in a Noetherian local ring (R, m) is the largest integer q such that Q : m is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x1 , x2 , . . . , xν ]] are characterized using the semigroup of R. This helps in computing them for classes of numerical semigroup rings, as well as on a case by case basis. The minimal Goto number of R and its connection to other invariants is explored. Necessary and sufficient conditions for the associated graded rings of R and R/x1R to be Gorenstein are also given, again using the semigroup.
منابع مشابه
Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module
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