PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 29(43), pp. 229239 (1981) 

THE REES CONGRUENCE IN UNIVERSAL ALGEBRASRobert F. TichyPatrubangasse 5, A1100 Vienna, AustriaAbstract: In the famous semigrouptheoretical 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 Full text of the article:
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