Free profinite locally idempotent and locally commutative semigroups

This paper is concerned with the structure of semigroups of implicit operat ions on the pseudo-variety LSI of finite locally idempotent and locally com mutative semigroups. We depart from a general result of Almeida and Weil to give two descriptions of these semigroups: the first in terms of infinite words, and the second in terms of infinite and bi-infinite words. We then d erive some applications. (C) 2001 Elsevier Science B.V. All rights reserved .