Reuben Spake, "The semigroup of nonempty finite subsets of integers", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 461819, 12 pages, 1986. https://doi.org/10.1155/S0161171286000765
The semigroup of nonempty finite subsets of integers
Let be the additive group of integers and the semigroup consisting of all nonempty finite subsets of with respect to the operation defined byFor , define to be the basis of and the basis of . In the greatest semilattice decomposition of , let denote the archimedean component containing and define . In this paper we examine the structure of and determine its greatest semilattice decomposition. In particular, we show that for , if and only if and . Furthermore, if is a non-singleton, then the idempotent-free is isomorphic to the direct product of the (idempotent-free) power joined subsemigroup and the group .
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