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The Congruence Lattice of Bruck–Reilly Extensions

The Congruence Lattice of Bruck–Reilly Extensions We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism α. The inclusion, meet and join of congruences are described in terms of congruences and ideals of T. We show that C(S) can be naturally decomposed into three sublattices, corresponding (roughly speaking) to the three different types of congruences on such semigroups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

The Congruence Lattice of Bruck–Reilly Extensions

Piochi, Brunetto
Algebra Colloquium , Volume 7 (1) – Jan 1, 2000
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14 pages

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0059-4
Publisher site
See Article on Publisher Site

Abstract

We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism α. The inclusion, meet and join of congruences are described in terms of congruences and ideals of T. We show that C(S) can be naturally decomposed into three sublattices, corresponding (roughly speaking) to the three different types of congruences on such semigroups.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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