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

 

Embedding general algebras into modules


Authors: Michał M. Stronkowski and David Stanovsky
Journal: Proc. Amer. Math. Soc. 138 (2010), 2687-2699
MSC (2010): Primary 08A05, 15A78, 16Y60
Published electronically: April 9, 2010
MathSciNet review: 2644885
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Abstract: The problem of embedding general algebras into modules is revisited. We provide a new method of embedding, based on Ježek's embedding into semimodules. We obtain several interesting consequences: a simpler syntactic characterization of quasi-affine algebras, a proof that quasi-affine algebras without nullary operations are actually quasi-linear, and several facts regarding the ``abelian iff quasi-affine'' problem.


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Additional Information

Michał M. Stronkowski
Affiliation: Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland – and – Eduard Čech Center, Charles University, Prague, Czech Republic
Email: m.stronkowski@mini.pw.edu.pl

David Stanovsky
Affiliation: Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Email: stanovsk@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10356-6
PII: S 0002-9939(10)10356-6
Keywords: Quasi-linear algebras, quasi-affine algebras, abelian algebras
Received by editor(s): August 14, 2009
Received by editor(s) in revised form: November 29, 2009
Published electronically: April 9, 2010
Additional Notes: The first author was supported by the Eduard Čech Center Grant LC505 and by the Statutory Grant of Warsaw University of Technology 504G11200112000
The second author was supported by the institutional grant MSM 0021620839 and by the GAČR Grant #201/08/P056.
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2010 American Mathematical Society