Weight ideals associated to regular and log-linear arrays. (March 2015)

• Record Type: Journal Article
• Authors: Johnson, Jeremiah W.
• Is Part Of: Journal of symbolic computation. Volume 67(2015)
• Page Start: 1
• Page End: 15
• Publication Date: 2015-03
• Subjects: Noncommutative Gröbner bases -- Gröbner bases -- Admissible orders; 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.2014.08.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Certain weight-based orders on the free associative algebra R = k 〈 x 1, …, x t 〉 can be specified by t × ∞ arrays whose entries come from the subring of positive elements in a totally ordered field. If such an array satisfies certain additional conditions, it produces a partial order on R which is an admissible order on the quotient R / I, where the ideal I is a homogeneous binomial ideal called the weight ideal associated to the array. The structure of the weight ideal is determined entirely by the array. This article discusses the structure of the weight ideals associated to two distinct types of arrays which define admissible orders on the associated quotient algebra.