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Parametric Decomposition of Monomial Ideals, II

✍ Scribed by William Heinzer; Ahmad Mirbagheri; L.J. Ratliff Jr.; Kishor Shah

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
324 KB
Volume
187
Category
Article
ISSN
0021-8693

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✦ Synopsis

monomial idea so I is generated by elements of the form x иии x , where each 1 d . Ž . e is a nonnegative integer . The main results of this paper: a establish a practical i Ž . formula which computes the monomial length of I when Rad I s ŽŽ . . Ž . Rad x , . . . , x R ; b determine necessary and sufficient conditions for the 1 d

Ž . intersection of finitely many monomial ideals to again be a monomial ideal; c show that if C, the set of all monomial ideals in R that contain I, is closed under finite intersections, then each ideal J in C has a unique decomposition as an Ž a 1 a h . irredundant finite intersection of ideals of the form x , . . . , x R, where is a Ž1. Ž h. Ä 4 Ä 4 permutation of 1, . . . , d , h g 1, . . . , d , and a , . . . , a are positive integers; and, 1 h Ž . d give additional results for certain form rings and Rees rings of R, related to the unique parametric decomposition theorem.

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