Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

2 Issues per year

CiteScore 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.208
Source Normalized Impact per Paper (SNIP) 2017: 0.322

Mathematical Citation Quotient (MCQ) 2017: 0.32

See all formats and pricing
More options …

How to compute the Wedderburn decomposition of a finite-dimensional associative algebra

Murray R. Bremner
Published Online: 2011-01-20 | DOI: https://doi.org/10.1515/gcc.2011.003


This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Rónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küronya and Wales. I illustrate these algorithms with the case n = 2 of the rational semigroup algebra of the partial transformation semigroup PTn on n elements; this generalizes the full transformation semigroup and the symmetric inverse semigroup, and these generalize the symmetric group Sn .

Keywords.: Structure theory of associative algebras; Dickson's Theorem on the radical; Wedderburn–Artin Theorem; Wedderburn–Malcev Theorem; computational algebra; finite transformation semigroups; representation theory of finite semigroups

About the article

Received: 2010-06-17

Published Online: 2011-01-20

Published in Print: 2011-05-01

Citation Information: Groups – Complexity – Cryptology, Volume 3, Issue 1, Pages 47–66, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc.2011.003.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Murray R. Bremner and Hader A. Elgendy
Linear and Multilinear Algebra, 2018, Page 1
Hader A. Elgendy
Communications in Algebra, 2014, Volume 42, Number 4, Page 1785
Murray Bremner and Sara Madariaga
Journal of Algebra, 2014, Volume 412, Page 51
Murray R. Bremner
Linear Algebra and its Applications, 2014, Volume 449, Page 381
Gábor Ivanyos, Lajos Rónyai, and Josef Schicho
Journal of Algebra, 2012, Volume 354, Number 1, Page 211

Comments (0)

Please log in or register to comment.
Log in