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L-subsemigroups of a free semigroup. (English) Zbl 0631.20048

The paper deals with certain meet-complete lattices of subsemigroups of a free semigroup. Such a lattice can be connected with a fuzzy or L-fuzzy semigroup [cf. the author, Ric. Mat. 33, 53-62 (1984; Zbl 0582.20037)] on a given free semigroup (the lattice of a-cuts). Considering lattices of free, pure, very pure, left unitary, right unitary and unitary semigroups [cf. G. Lallement, Semigroups and combinatorial applications (1979; Zbl 0421.20025)], the author leads to suitable conditions for the respective fuzzy semigroups.
Reviewer: J.Drewniak

MSC:

20M05 Free semigroups, generators and relations, word problems
08A30 Subalgebras, congruence relations
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