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Universal Algebra and Lattice Theory (Dedicated to the 70th birthday of B. Csakany)
July 22-26, 2002
University of Szeged
Szeged, Hungary |
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Organizers
Agnes Szendrei, Laszlo Szabo, Miklos Dorman
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Balanced Semidirect Products and its Endomorphisms
by
Vitaliy M. Usenko
Dept. of Algebra and Analysis, Lugansk State Pedagogical Taras Shevchenko University, Ukraine
Let (M1, *), (M2, *) - monoids, for which homorphism
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\rho:M1 --> T(M2):t --> \rhot |
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and antihomomorphism
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\lambda:M2 --> T(M2):t --> \lambdat |
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are determined (T(X) is symmetric semigroup on the set
X here). Then the balanced semidirect product
[\rho:M1×M2:\lambda] of M1 and M2,
consists of the set M1×M2 equipped product
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(x;t)*(y;t)=(x*y\lambdat;t\rhoy*u) |
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The homomorphisms of the balanced semidirect products and its
endomorphisms semigroups are described in the terms of the
semiretractions that was inroduced in [1].
1. Usenko V.M. The semiretractions of monoids,
Proceeding of IAMM NSA of Ukraine. - 2000. - v.5.- p.155-164.
Date received: July 3, 2002
Copyright © 2002 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caiv-43.