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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.

MSC:
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
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References:
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