Abstract
Eilenberg has shown that there is a one-to-one correspondence between varieties of finite monoids and varieties of recognizable languages. In this paper, we give a description of a variety of languages close to the class of piecewise testable languages considered by I. Simon. The corresponding variety of monoids is the variety of j -trivial monoids with commuting idempotents. This result is then generalized to the case of finite monoids with commuting idempotents whose regular D -classes are groups from a given variety of groups.
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