Monomial right ideals and the Hilbert series of noncommutative modules

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• 作者：Roberto La Scala¹ ; ^{roberto.lascala@uniba.it}
• 关键词：primary ; 16Z05 ; secondary ; 16P90 ; 05A15
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：May-June 2017
• 年：2017
• 卷：80
• 期：part_P2
• 页码：403-415
• 全文大小：365 K
• 卷排序：80

文摘

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〈x1,…,xn〉K〈x1,…,xn〉. 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.