Abstract
In papers of one of the authors there were introduced quasiregular algebras over semigroups and their important role was advanced in language-theory research (cf. [1] and its accompanying bibliography). In particular, it was proven that quasiregular algebras over free semigroups give an algebraic characteristic to the class of contextfree languages similar to that which is given by regular Kleene algebras to the class of finite-automaton languages. All this made the problem of investigating quasiregular algebras over some semigroups or other an interesting and important one. Of particular interest here, as should be expected, is the identity problem for these algebras.
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