2021/07/31 by Dibyendu De, De, Dibyendu, Pintu Debnath +3
Mathematics · Computer Science · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2108.05200
There is a long history of studying Ramsey theory using the algebraic structure of the Stone-Čech compactification of discrete semigroup. It has been shown that various Ramsey theoretic structures are contained in different algebraic large sets. In this article we will deduce the combinatorial characterization of certain sets, that are the member of the idempotent ultrafilters of the closed subsemigroup of βS, arising from certain Ramsey family. In a special case when S=ℕ, we will deduce that sets which are the members of all idempotent ultrafilters of those semigroups contain certain additive-multiplicative structures. Later we will generalize this result for weak rings, where we will show a non-commutative version of the additive-multiplicative structure.