Math 2.0

General algebraic systems Mal'cev conditions Concept

Mal'cev term

Summary

A Mal'cev term of a variety is a ternary term pp such that p(x,y,y)=xp(x, y, y) = x and p(x,x,y)=yp(x, x, y) = y hold in the variety. By Mal'cev's theorem, a variety has a Mal'cev term exactly when it is a congruence-permutable variety. Groups, rings, modules and quasigroups all have Mal'cev terms.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Congruence-permutable_algebra
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Changed2 November 2026

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