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Decompositions of graphs of modules over semisimple rings

Published online by Cambridge University Press:  17 April 2009

Grace Orzech
Grace Orzech
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston K7L 3N6, Canada.
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In this paper we show that an R-module graph over a semisimple ring R can be written as a direct sum of graphic submodules that are uniquely determined up to isomorphism type. Moreover, this decomposition enables us to describe the R-module graph in graphic terms as a disjoint union of connected components, each of which consists of a complete directed graph on its vertices together with a set of loops at each vertex, determined by the loops at 0. We also give a graphic version of Maschke's Theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 405 - 413
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Curtis, C.W. and Reiner, I., Representation theory of finite groups and associative algebras (Interscience Publishers, 1962.)Google Scholar
[2]Orzech, G., “R-module graphs”, preprint.Google Scholar
[3]Orzech, G., “A graph theoretic description of vector spaces with three subspaces”, preprint.Google Scholar
[4]Ribenboim, P., “Algebraic structures on graphs”. Algebra Universalis, 16 (1983), 105–123.Google Scholar
[5]Ribenboim, P., “Vector space graphs”, Nanta Math. 12 (1979), 125–132.Google Scholar