Abstract
Prelanguages and pregrammars introduced in [8] present a generalization of languages and pure grammars. Relation of domination and double domination may be easily transferred from languages to prelanguages. In the present paper submonoids of a commutative monoid are characterized by means of their relations of domination; subgroups of a commutative group are characterized by means of their relations of double domination. The submonoid generated by a subset of a commutative monoid is constructed using a suitable pregrammar.
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