Fraser-Horn identities can be written in two variables
A Mal'cev condition for varieties with directly decomposable congruences (DDC) was given by \textit{G. A. Fraser} and \textit{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.
Mal'cev condition for varieties with directly decomposable congruences
scientific article; zbMATH DE number 4095534