Infinite products in monoids (Q1080960)

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.