Powers of monomial ideals and the Ratliff–Rush operation. (May 2021)

• Record Type: Journal Article
• Authors: Gasanova, Oleksandra
• Is Part Of: Journal of symbolic computation. Volume 104(2021)
• Page Start: 69
• Page End: 89
• Publication Date: 2021-05
• Subjects: Ratliff–Rush operation -- Powers of monomial ideals -- Polynomial rings; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.04.002
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Powers of (monomial) ideals is a subject that still calls attraction in various ways. In this paper we present a nice presentation of high powers of ideals in a certain class in K [ x 1, …, x n ] and K [ [ x 1, …, x n ] ] . As an interesting application it leads to an algorithm for computation of the Ratliff–Rush operation on ideals in that class. The Ratliff–Rush operation itself has several applications, for instance, if I is a regular m -primary ideal in a local ring ( R, m ), then the Ratliff–Rush associated ideal I ˜ is the unique largest ideal containing I with the same Hilbert polynomial as I .