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- W2964214245 abstract "For every discrete semigroup S, the space βS (the Stone–Čech compactification of S) has a natural, right-topological semigroup structure extending S. Under some mild conditions, U(S), the set of uniform ultrafilters on S, is a two-sided ideal of βS, and therefore contains all of its minimal left ideals and minimal idempotents. Our main theorem states that, if S satisfies some mild distributivity conditions, U(S) contains prime minimal left ideals and left-maximal idempotents. If S is countable, then U(S)=S⁎, and a special case of our main theorem is that if a countable discrete semigroup S is weakly cancellative and left-cancellative, then S⁎=βS∖S contains prime minimal left ideals and left-maximal idempotents. We will provide examples of weakly cancellative semigroups where these conclusions fail, thus showing that this result is fairly sharp." @default.
- W2964214245 created "2019-07-30" @default.
- W2964214245 creator A5078515729 @default.
- W2964214245 date "2018-03-01" @default.
- W2964214245 modified "2023-10-18" @default.
- W2964214245 title "Ideals and idempotents in the uniform ultrafilters" @default.
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- W2964214245 doi "https://doi.org/10.1016/j.topol.2018.01.012" @default.
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