no. 3
On varieties of literally idempotent languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 583-598.

A language L⊆A * is literally idempotent in case that ua 2 v∈L if and only if uav∈L, for each u,v∈A * , a∈A. Varieties of literally idempotent languages result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator on classes of languages. We initiate the systematic study of such varieties. Various classes of literally idempotent languages can be characterized using syntactic methods. A starting example is the class of all finite unions of B 1 * B 2 * ⋯B k * where B 1 ,⋯,B k are subsets of a given alphabet A.

DOI : 10.1051/ita:2008020
Classification : 68Q45
Mots clés : literally idempotent languages, varieties of languages 
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     title = {On varieties of literally idempotent languages},
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     publisher = {EDP-Sciences},
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Klíma, Ondřej; Polák, Libor. On varieties of literally idempotent languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 583-598. doi : 10.1051/ita:2008020. http://archive.numdam.org/articles/10.1051/ita:2008020/

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