Matches in SemOpenAlex for { <https://semopenalex.org/work/W203410093> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W203410093 abstract "The simplest multiplicative systems in which arithmeticalideas can be defined are semigroups. For such systems irreducible(prime) elements can be introduced and conditions underwhich the fundamental theorem of arithmetic holds have been investigated(Clifford (3)). After identifying associates, the elementsof the semigroup form a partially ordered set with respectto the ordinary division relation. This suggests the possibilityof an analogous arithmetical result for abstract partially orderedsets. Although nothing corresponding to product exists ina partially ordered set, there is a notion similar to g.c.d.This is the meet operation, defined as greatest lower bound.Thus irreducible elements, namely those elements not expressibleas meets of proper divisors can be introduced. The assumptionof the ascending chain condition then implies that each elementis representable as a reduced meet of irreducibles. The centralproblem of this thesis is to determine conditions on the structureof the partially ordered set in order that each elementhave a unique such representation. Part I contains preliminary results and introduces the principaltools of the investigation. In the second part, basic propertiesof the lattice of ideals and the connection between itsstructure and the irreducible decompositions of elements are developed.The proofs of these results are identical with the correspondingones for the lattice case (Dilworth (2)). The lastpart contains those results whose proofs are peculiar to partiallyordered sets and also contains the proof of the main theorem." @default.
- W203410093 created "2016-06-24" @default.
- W203410093 creator A5047633101 @default.
- W203410093 date "1950-01-01" @default.
- W203410093 modified "2023-09-27" @default.
- W203410093 title "An arithmetical theorem for partially ordered sets" @default.
- W203410093 doi "https://doi.org/10.7907/tp0k-a379." @default.
- W203410093 hasPublicationYear "1950" @default.
- W203410093 type Work @default.
- W203410093 sameAs 203410093 @default.
- W203410093 citedByCount "2" @default.
- W203410093 countsByYear W2034100932013 @default.
- W203410093 countsByYear W2034100932018 @default.
- W203410093 crossrefType "dissertation" @default.
- W203410093 hasAuthorship W203410093A5047633101 @default.
- W203410093 hasConcept C108710211 @default.
- W203410093 hasConcept C112343008 @default.
- W203410093 hasConcept C113429393 @default.
- W203410093 hasConcept C114614502 @default.
- W203410093 hasConcept C116335209 @default.
- W203410093 hasConcept C118615104 @default.
- W203410093 hasConcept C121332964 @default.
- W203410093 hasConcept C134306372 @default.
- W203410093 hasConcept C144901957 @default.
- W203410093 hasConcept C17744445 @default.
- W203410093 hasConcept C180375552 @default.
- W203410093 hasConcept C180645754 @default.
- W203410093 hasConcept C199539241 @default.
- W203410093 hasConcept C200288055 @default.
- W203410093 hasConcept C202444582 @default.
- W203410093 hasConcept C24890656 @default.
- W203410093 hasConcept C2524010 @default.
- W203410093 hasConcept C2781204021 @default.
- W203410093 hasConcept C33923547 @default.
- W203410093 hasConcept C42747912 @default.
- W203410093 hasConceptScore W203410093C108710211 @default.
- W203410093 hasConceptScore W203410093C112343008 @default.
- W203410093 hasConceptScore W203410093C113429393 @default.
- W203410093 hasConceptScore W203410093C114614502 @default.
- W203410093 hasConceptScore W203410093C116335209 @default.
- W203410093 hasConceptScore W203410093C118615104 @default.
- W203410093 hasConceptScore W203410093C121332964 @default.
- W203410093 hasConceptScore W203410093C134306372 @default.
- W203410093 hasConceptScore W203410093C144901957 @default.
- W203410093 hasConceptScore W203410093C17744445 @default.
- W203410093 hasConceptScore W203410093C180375552 @default.
- W203410093 hasConceptScore W203410093C180645754 @default.
- W203410093 hasConceptScore W203410093C199539241 @default.
- W203410093 hasConceptScore W203410093C200288055 @default.
- W203410093 hasConceptScore W203410093C202444582 @default.
- W203410093 hasConceptScore W203410093C24890656 @default.
- W203410093 hasConceptScore W203410093C2524010 @default.
- W203410093 hasConceptScore W203410093C2781204021 @default.
- W203410093 hasConceptScore W203410093C33923547 @default.
- W203410093 hasConceptScore W203410093C42747912 @default.
- W203410093 hasLocation W2034100931 @default.
- W203410093 hasOpenAccess W203410093 @default.
- W203410093 hasPrimaryLocation W2034100931 @default.
- W203410093 hasRelatedWork W100330389 @default.
- W203410093 hasRelatedWork W1202721983 @default.
- W203410093 hasRelatedWork W1559687517 @default.
- W203410093 hasRelatedWork W1967047978 @default.
- W203410093 hasRelatedWork W2005135052 @default.
- W203410093 hasRelatedWork W2010757891 @default.
- W203410093 hasRelatedWork W2013726652 @default.
- W203410093 hasRelatedWork W2067039034 @default.
- W203410093 hasRelatedWork W2068318851 @default.
- W203410093 hasRelatedWork W2119264607 @default.
- W203410093 hasRelatedWork W2130256938 @default.
- W203410093 hasRelatedWork W2152361896 @default.
- W203410093 hasRelatedWork W2329985525 @default.
- W203410093 hasRelatedWork W24652474 @default.
- W203410093 hasRelatedWork W2758696579 @default.
- W203410093 hasRelatedWork W3021320463 @default.
- W203410093 hasRelatedWork W3023411169 @default.
- W203410093 hasRelatedWork W46733651 @default.
- W203410093 hasRelatedWork W52557785 @default.
- W203410093 hasRelatedWork W93968053 @default.
- W203410093 isParatext "false" @default.
- W203410093 isRetracted "false" @default.
- W203410093 magId "203410093" @default.
- W203410093 workType "dissertation" @default.