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On Varieties of Literally Idempotent Languages

Ondřej Klíma, Libor Polák (2008)

RAIRO - Theoretical Informatics and Applications

A language L ⊆A* is literally idempotent in case that ua2v ∈ 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...

One-sided principal ideals in the direct product of two semigroups

Imrich Fabrici (1993)

Mathematica Bohemica

A necessary and sufficient condition is given for a) a principal left ideal L ( s , t ) in S × T to be equal to the direct product of the corresponding principal left ideals L ( s ) × L ( t ) , b) an -class L ( s , t ) to be equal to the direct product of the corresponding -classes L s × L t .

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