Monomial right ideals and the Hilbert series of noncommutative modules. (May 2017)

• Record Type: Journal Article
• Authors: La Scala, Roberto
• Is Part Of: Journal of symbolic computation. Volume 80:Part 2(2017)
• Page Start: 403
• Page End: 415
• Publication Date: 2017-05
• Subjects: primary 16Z05 -- secondary 16P90 05A15; Hilbert series -- Noncommutative modules -- Automata; 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.2016.07.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper we present a procedure for computing the rational sum of the Hilbert series of a finitely generated monomial right module N over the free associative algebra K 〈 x 1, …, x n 〉 . We show that such procedure terminates, that is, the rational sum exists, when all the cyclic submodules decomposing N are annihilated by monomial right ideals whose monomials define regular formal languages. The method is based on the iterative application of the colon right ideal operation to monomial ideals which are given by an eventual infinite basis. By using automata theory, we prove that the number of these iterations is a minimal one. In fact, we have experimented efficient computations with an implementation of the procedure in Maple which is the first general one for noncommutative Hilbert series.