Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4945965 | Journal of Symbolic Computation | 2017 | 13 Pages |
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 Kãx1,â¦,xnã. 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.
Related Topics
Physical Sciences and Engineering
Computer Science
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Authors
Roberto La Scala,