EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 29(43), pp. 229--239 (1981)

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THE REES CONGRUENCE IN UNIVERSAL ALGEBRAS

Robert F. Tichy

Patrubangasse 5, A-1100 Vienna, Austria

Abstract: In the famous semigroup-theoretical paper of D. Rees (1940) the author introduced a special congruence for semigroups and proved some fundamental isomorphism theorems. We generalize the ideas of Rees to universal algebras and introduce the notion of Rees congruence in a universal algebra. We prove an isomorphism theorem and apply it to study the notion of Rees series in universal algebras; this is a generalization of the notion of normal series in group theory. Further we study the structure of the set of all Rees congrunces and in the last part of the paper we present some applications of this theory to algebras of polynomial functions.

Classification (MSC2000): 08A25

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Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition