Journal of Mathematical Sciences

, Volume 185, Issue 3, pp 484–496 | Cite as

Dimension polynomials in the generalized difference case

  • S. N. Smirnov


The aim of this paper is to generalize results on dimension polynomials of difference modules over difference rings for a wider class of rings of difference operators. We introduce the notion of quasi-commutativity, which generalizes the notion of commutativity and enables one to consider wider classes of monoids and groups of endomorphisms. Some properties of quasi-commutative monoids and groups are established; these properties allow us to apply some methods that are almost similar to the ones used in working with free commutative monoids and groups. Also we prove the theorem of existence of the dimension polynomial of generalized difference modules in the cases where the submonoid of endomorphisms is free quasi-commutative. Also the existence of its analog for the case of a direct product of a free quasi-commutative monoid and a finite cyclic group is established.


Exact Sequence Cyclic Group Commutative Ring Characteristic Polynomial Induction Statement 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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