Intersection of Ideals with Non-commutative Subalgebras

Viktor Levandovskyy

Intersection of Ideals with Non-commutative Subalgebras

Viktor Levandovskyy

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Computation of an intersection of a left ideal with a subalgebra, which is not fully investigated until now, is important for different areas of mathematics. We present an algorithm for the computation of the preimage of a left ideal under a morphism of non--commutative $GR$--algebras, and show both its abilities and limitations. The main computational tools are the elimination of variables by means of Gröobner bases together with the constructive treatment of opposite algebras and the utilization of a special bimodule structure.

Original language	English
Title of host publication	Proceedings of the ISSAC 2006 Conference
Editors	Jean-Guillaume Dumas
Publisher	ACM Press
Number of pages	8
ISBN (Print)	1-59593-095-7
Publication status	Published - Jul 2006

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

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abstract = "Computation of an intersection of a left ideal with a subalgebra, which is not fully investigated until now, is important for different areas of mathematics. We present an algorithm for the computation of the preimage of a left ideal under a morphism of non--commutative \$GR\$--algebras, and show both its abilities and limitations. The main computational tools are the elimination of variables by means of Gr{\"o}obner bases together with the constructive treatment of opposite algebras and the utilization of a special bimodule structure.",

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