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A note on homotopy in universal algebra. (English) Zbl 0844.08008

Summary: Necessary and sufficient conditions are given under which an algebra with one \(n\)-ary operation \((n\geq 2)\) is isotopic to an algebra with unit. The main theorem gives a generalization of well-known Albert’s theorem.

MSC:

08A99 Algebraic structures
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References:

[1] Petrescu A.: On the homotopy of universal algebra. Revue Roum. Math. Pures Et Appl., 22, No 4, 1977. · Zbl 0357.08005
[2] Albert A. A.: Quasigroups. I. Trans. Amer. Math. Soc., 54 (1943), 507-519. · Zbl 0063.00039 · doi:10.2307/1990259
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