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Duda, Jaromír

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

Algebra Univers. 26, No. 2, 178-180 (1989).
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

Cited in 4 Documents

MSC:

08B05 Equational logic, Mal’tsev conditions

Keywords:

Mal’cev condition for varieties with directly decomposable congruences; identities

Citations:

Zbl 0241.08004
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\textit{J. Duda}, Algebra Univers. 26, No. 2, 178--180 (1989; Zbl 0669.08003)
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References:

[1] J. Duda,On two schemes applied to Mal’cev type theorems, Ann. Univ. Sci. Budapest, Sectio Math.26 (1983), 39-45. · Zbl 0518.08002
[2] J. Duda,Varieties having directly decomposable congruence classes, ?asopis p?st, matem.111 (1986), 394-403. · Zbl 0606.08001
[3] J. Duda,Congruences on products in varieties satisfying the CEP, Math. Slovaca36 (1986), 171-177. · Zbl 0598.08005
[4] G. A. Fraser andA. Horn,Congruence relations in direct products, Proc. Amer. Math. Soc.26 (1970), 390-394. · Zbl 0241.08004
[5] G. Gr?tzer,Universal Algebra,Second Expanded Edition, Springer Verlag, Berlin, Heidelberg and New York, 1979.
[6] J.Hagemann,Congruences on products and subdirect products of algebras, Preprint Nr. 219, TH-Darmstadt, 1975.
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