GOTO NUMBERS OF A NUMERICAL SEMIGROUP RING AND THE GORENSTEINESS OF ASSOCIATED GRADED RINGS

被引：20
|
作者：
Bryant, Lance [1 ]
机构：
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
来源：
COMMUNICATIONS IN ALGEBRA | 2010年 / 38卷 / 06期
关键词：
Associated graded ring; Gorenstein; Integral closure; Numerical semigroup; Quasi-socle ideal; LINKS;
D O I：
10.1080/00927870903025993
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Goto number of a parameter ideal Q in a Noetherian local ring (R, m) is the largest integer q such that Q : m(q) is integral over Q. The Goto numbers of the monomial parameter ideals of R = k [[x(a1),x(a2), . . . , x(av)]] 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/x(a1) R to be Gorenstein are also given, again using the semigroup of R.
引用
收藏
页码：2092 / 2128
页数：37
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