## Permutability of congruences in varieties with idempotent operations.(English)Zbl 0768.08006

Author’s summary: It is proven that if a variety $$V$$ with at least two binary idempotent operations $$f$$, $$g$$ is permutable, then there exists a ternary term $$t(x,y,z)$$ such that $$t(x,x,z)=f(x,z)$$ and $$t(x,z,z)=g(x,z)$$. If, moreover, reducts of algebras of $$V$$ are lattices, this condition is necessary and sufficient for the permutability of $$V$$.
Reviewer: R.A.Alo (Houston)

### MSC:

 08B05 Equational logic, Mal’tsev conditions 08A30 Subalgebras, congruence relations
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### References:

 [1] Grätzer G.: General Lattice Theory. Berlin, 1978. · Zbl 0436.06001 [2] Maľcev A.I.: On the general theory of algebraic systems. (Russian), Matem.Sbornik 35 (1954), 3-20.
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