Abstract
T. Dent, K. Kearnes and A. Szendrei have defined the derivative, Σ′, of a set of equations Σ and shown, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent $${(\Sigma^\prime \models x \approx y)}$$ . In this paper we investigate other types of derivatives that give similar results for congruence n-permutability for some n, and for congruence semidistributivity.
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