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Infinite products in monoids. (English) Zbl 0601.20061
For any monoid M in a certain class containing the abelian monoids and the groups, a monoid structure is constructed on some quotient set of \(M^{{\mathbb{N}}}\), the set of all \({\mathbb{N}}\)-indexed sequences in M. Moreover this monoid is endowed with infinitary products extending its binary law in a natural way. Applications of these constructions in set theory and computer science are outlined.

20M35 Semigroups in automata theory, linguistics, etc.
03D05 Automata and formal grammars in connection with logical questions
68Q45 Formal languages and automata
20M15 Mappings of semigroups
Full Text: DOI EuDML
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