PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 29(43), pp. 229--239 (1981)
THE REES CONGRUENCE IN UNIVERSAL ALGEBRAS
Robert F. TichyPatrubangasse 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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