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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The complexity of the word-problem for finite matrix rings


Authors: Csaba Szabó and Vera Vértesi
Journal: Proc. Amer. Math. Soc. 132 (2004), 3689-3695
MSC (2000): Primary 68Q17, 03C13
Published electronically: July 20, 2004
MathSciNet review: 2084092
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Abstract: We analyze the so-called word-problem for $M_2(Z_2)$, the ring of $2\times 2$ matrices over $Z_2$. We prove that the term-equivalence problem for the semigroup (and so for the ring) $M_2(Z_2)$ is coNP-complete.


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Additional Information

Csaba Szabó
Affiliation: Department of Algebra and Number Theory, Eötvös Loránd University, 1117 Budapest, Pázmány Péter sétány 1/c, Hungary
Email: csaba@cs.elte.hu

Vera Vértesi
Affiliation: Department of Algebra and Number Theory, Eötvös Loránd University, 1117 Budapest, Pázmány Péter sétány 1/c, Hungary
Email: wera13@cs.elte.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07488-X
PII: S 0002-9939(04)07488-X
Keywords: 0-simple semigroup, term, complexity
Received by editor(s): September 5, 2002
Received by editor(s) in revised form: July 24, 2003
Published electronically: July 20, 2004
Communicated by: Lance W. Small
Article copyright: © Copyright 2004 American Mathematical Society