ABSTRACT
In this first chapter we will briefly review the main concepts and results of Universal Algebra, without any proofs. Details can be found in any standard book on Universal Algebra; see for example [23], [26], [100], [142], [116] or [130].
1.1 Algebras An algebra is a nonempty set together with a set of finitary operations defined on this set. Let A be any set, and let n be a positive integer. Then the n — th cartesian power of A is denoted by An, with typical elements a := (a i , . . . , an). An n-ary operation on >1 is a function f A : A n —► A. The only restriction in our approach is that the fundamental operations of an algebra have to be at least 1-ary. (We may regard any 0-ary operation as a constant 1-ary one.) It is customary to refer to 1-ary, 2-ary, or 3-ary operations as unary, binary, or ternary, respectively.
