zbMATH — the first resource for mathematics

Infinite iteration of matrix semigroups. I: Structure theorem for torsion semigroups. (English) Zbl 0584.20053
The main result of this paper is a representation theorem for countable torsion monoids, that is, countable monoids in which every element is of finite order. Every such monoid T is the homomorphic image \(\sigma\) (S) of a torsion monoid S with S and \(\sigma\) having several special properties some of which can be roughly described as follows: S is obtained by an infinitely iterated sandwich matrix type of construction based on certain cyclic submonoids of T and on translations of finite subsets of T. The morphism \(\sigma\) is of a restricted kind, defined along with the matrix construction. The maximal subgroups of S are finite cyclic groups and the restriction of \(\sigma\) to these is injective. S can be characterized as an elementary projective limit of finitely iterated matrix semigroups.
Reviewer: H.J├╝rgensen

20M10 General structure theory for semigroups
20M20 Semigroups of transformations, relations, partitions, etc.
20M15 Mappings of semigroups
20M30 Representation of semigroups; actions of semigroups on sets
Full Text: DOI
[1] Clifford, A.H; Preston, G.B, ()
[2] Eilenberg, S, ()
[3] Krohn, K; Rhodes, J; Tilson, B, (), Chapters 1, and 5-9
[4] Lallement, G, Semigroups and combinatorial applications, (1979), Wiley New York · Zbl 0421.20025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.