Matches in SemOpenAlex for { <https://semopenalex.org/work/W4288050002> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W4288050002 endingPage "108608" @default.
- W4288050002 startingPage "108608" @default.
- W4288050002 abstract "We show that for every n∈N, the semigroup βN, the Stone-Čech compactification of the natural numbers, contains an element of order n, that is, an element p such that all ip=p+…+p︸i, where i∈{1,…,n}, are distinct and (n+1)p=np. This is a complete solution to a long standing open problem. In fact, we prove that for any m≥1 and n≥2, there are distinct elements p=p1, p2…,pm in βN of order n such that ps+pt=2p for all s,t∈{1,…,m}. As a consequence we obtain a new Ramsey theoretic result: there is a partition {A1,s:s∈{1,…,m}}∪{Ai:i∈{2,…,n}} of N such that, whenever for each i∈{2,…,n} Ri is a finite partition of Ai, there exist Bi∈Ri and a sequence (xk)k=1∞ such that xk∈A1,sk∩2kN, where sk≡k(modm), and for each finite F⊆N with |F|≥2, if |F|=i<n, then ∑k∈Fxk∈Bi, and if |F|≥n, then ∑k∈Fxk∈Bn." @default.
- W4288050002 created "2022-07-27" @default.
- W4288050002 creator A5010302050 @default.
- W4288050002 date "2022-10-01" @default.
- W4288050002 modified "2023-10-06" @default.
- W4288050002 title "Elements of finite order in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:mi>β</mml:mi><mml:mi mathvariant=double-struck>N</mml:mi></mml:math>" @default.
- W4288050002 cites W2010069811 @default.
- W4288050002 cites W2036509702 @default.
- W4288050002 cites W3044148139 @default.
- W4288050002 cites W3118713850 @default.
- W4288050002 doi "https://doi.org/10.1016/j.aim.2022.108608" @default.
- W4288050002 hasPublicationYear "2022" @default.
- W4288050002 type Work @default.
- W4288050002 citedByCount "1" @default.
- W4288050002 crossrefType "journal-article" @default.
- W4288050002 hasAuthorship W4288050002A5010302050 @default.
- W4288050002 hasConcept C10138342 @default.
- W4288050002 hasConcept C114614502 @default.
- W4288050002 hasConcept C118615104 @default.
- W4288050002 hasConcept C162324750 @default.
- W4288050002 hasConcept C182306322 @default.
- W4288050002 hasConcept C207405024 @default.
- W4288050002 hasConcept C33923547 @default.
- W4288050002 hasConcept C42812 @default.
- W4288050002 hasConceptScore W4288050002C10138342 @default.
- W4288050002 hasConceptScore W4288050002C114614502 @default.
- W4288050002 hasConceptScore W4288050002C118615104 @default.
- W4288050002 hasConceptScore W4288050002C162324750 @default.
- W4288050002 hasConceptScore W4288050002C182306322 @default.
- W4288050002 hasConceptScore W4288050002C207405024 @default.
- W4288050002 hasConceptScore W4288050002C33923547 @default.
- W4288050002 hasConceptScore W4288050002C42812 @default.
- W4288050002 hasLocation W42880500021 @default.
- W4288050002 hasOpenAccess W4288050002 @default.
- W4288050002 hasPrimaryLocation W42880500021 @default.
- W4288050002 hasRelatedWork W1978202015 @default.
- W4288050002 hasRelatedWork W1987931249 @default.
- W4288050002 hasRelatedWork W2005827783 @default.
- W4288050002 hasRelatedWork W2031004667 @default.
- W4288050002 hasRelatedWork W2145358719 @default.
- W4288050002 hasRelatedWork W2317457021 @default.
- W4288050002 hasRelatedWork W3025390008 @default.
- W4288050002 hasRelatedWork W3086542228 @default.
- W4288050002 hasRelatedWork W3098379097 @default.
- W4288050002 hasRelatedWork W4280511095 @default.
- W4288050002 hasVolume "408" @default.
- W4288050002 isParatext "false" @default.
- W4288050002 isRetracted "false" @default.
- W4288050002 workType "article" @default.
