Fraser-Horn identities can be written in two variables. (English) Zbl 0669.08003

A Mal’cev condition for varieties with directly decomposable congruences (DDC) was given by G. A. Fraser and A. Horn [Proc. Am. Math. Soc. 26, 390-394 (1970; Zbl 0241.08004)]. The identities they used involved three variables, being built up from binary, ternary, and \(m+1\)- ary terms. This paper provides a system of identities involving only two variables, being built up from binary and \(m+2\)-ary terms. As a consequence of this we have the result that a variety \({\mathcal V}\) has DDC if and only if \(F_{{\mathcal V}}(2)\times F_{{\mathcal V}}(2)\) has DDC.
Reviewer: S.Oates-Williams


08B05 Equational logic, Mal’tsev conditions


Zbl 0241.08004
Full Text: DOI


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