Matches in SemOpenAlex for { <https://semopenalex.org/work/W2324844435> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W2324844435 abstract "In classical geometric algebra, there have been several treatments of affine and projective planes based on fields. In this thesis we approach affine and projective planes from a constructive point of view and we base our geometry on local rings instead of fields. We start by constructing projective and affine planes over local rings and establishing forms of Desargues' Theorem and Pappus' Theorem which hold for these. From this analysis we derive coherent theories of projective and affine planes. The great Greek mathematicians of the classical period used geometry as the basis for their theory of quantities. The modern version of this idea is the reconstruction of algebra from geometry. We show how we can construct a local ring whenever we are given an affine or a projective plane. This enables us to describe the classifying toposes of our theories of affine and projective planes as extensions of the Zariski topos by certain group actions. Through these descriptions of the classifying toposes, the links between the theories of local rings, affine and projective planes become clear. In particular, the geometric morphisms between these classifying toposes are all induced by group homomorphisms even though they demonstrate complicated constructions in geometry. In this thesis, we also prove results in topos theory which are applied to these geometric morphisms to give Morita equivalences between some further theories." @default.
- W2324844435 created "2016-06-24" @default.
- W2324844435 creator A5028982992 @default.
- W2324844435 date "2016-01-19" @default.
- W2324844435 modified "2023-10-01" @default.
- W2324844435 title "A constructive approach to affine and projective planes" @default.
- W2324844435 cites W1518129101 @default.
- W2324844435 cites W1580648567 @default.
- W2324844435 cites W1594900487 @default.
- W2324844435 cites W1985873720 @default.
- W2324844435 cites W1999813004 @default.
- W2324844435 cites W2009414585 @default.
- W2324844435 cites W2021819349 @default.
- W2324844435 cites W2033961179 @default.
- W2324844435 cites W2052923646 @default.
- W2324844435 cites W2053938049 @default.
- W2324844435 cites W2916821289 @default.
- W2324844435 cites W2963333202 @default.
- W2324844435 cites W951059644 @default.
- W2324844435 hasPublicationYear "2016" @default.
- W2324844435 type Work @default.
- W2324844435 sameAs 2324844435 @default.
- W2324844435 citedByCount "4" @default.
- W2324844435 countsByYear W23248444352019 @default.
- W2324844435 countsByYear W23248444352020 @default.
- W2324844435 crossrefType "posted-content" @default.
- W2324844435 hasAuthorship W2324844435A5028982992 @default.
- W2324844435 hasConcept C117220453 @default.
- W2324844435 hasConcept C124952713 @default.
- W2324844435 hasConcept C136119220 @default.
- W2324844435 hasConcept C137212723 @default.
- W2324844435 hasConcept C142362112 @default.
- W2324844435 hasConcept C163434512 @default.
- W2324844435 hasConcept C173110770 @default.
- W2324844435 hasConcept C177846678 @default.
- W2324844435 hasConcept C182141236 @default.
- W2324844435 hasConcept C185362025 @default.
- W2324844435 hasConcept C202444582 @default.
- W2324844435 hasConcept C23684344 @default.
- W2324844435 hasConcept C2524010 @default.
- W2324844435 hasConcept C33923547 @default.
- W2324844435 hasConcept C39290043 @default.
- W2324844435 hasConcept C68363185 @default.
- W2324844435 hasConcept C75280867 @default.
- W2324844435 hasConcept C92757383 @default.
- W2324844435 hasConceptScore W2324844435C117220453 @default.
- W2324844435 hasConceptScore W2324844435C124952713 @default.
- W2324844435 hasConceptScore W2324844435C136119220 @default.
- W2324844435 hasConceptScore W2324844435C137212723 @default.
- W2324844435 hasConceptScore W2324844435C142362112 @default.
- W2324844435 hasConceptScore W2324844435C163434512 @default.
- W2324844435 hasConceptScore W2324844435C173110770 @default.
- W2324844435 hasConceptScore W2324844435C177846678 @default.
- W2324844435 hasConceptScore W2324844435C182141236 @default.
- W2324844435 hasConceptScore W2324844435C185362025 @default.
- W2324844435 hasConceptScore W2324844435C202444582 @default.
- W2324844435 hasConceptScore W2324844435C23684344 @default.
- W2324844435 hasConceptScore W2324844435C2524010 @default.
- W2324844435 hasConceptScore W2324844435C33923547 @default.
- W2324844435 hasConceptScore W2324844435C39290043 @default.
- W2324844435 hasConceptScore W2324844435C68363185 @default.
- W2324844435 hasConceptScore W2324844435C75280867 @default.
- W2324844435 hasConceptScore W2324844435C92757383 @default.
- W2324844435 hasLocation W23248444351 @default.
- W2324844435 hasOpenAccess W2324844435 @default.
- W2324844435 hasPrimaryLocation W23248444351 @default.
- W2324844435 hasRelatedWork W111918409 @default.
- W2324844435 hasRelatedWork W1578034544 @default.
- W2324844435 hasRelatedWork W1594208273 @default.
- W2324844435 hasRelatedWork W1977857281 @default.
- W2324844435 hasRelatedWork W2095056918 @default.
- W2324844435 hasRelatedWork W2121857197 @default.
- W2324844435 hasRelatedWork W2133314801 @default.
- W2324844435 hasRelatedWork W2150525570 @default.
- W2324844435 hasRelatedWork W2220654239 @default.
- W2324844435 hasRelatedWork W2242216162 @default.
- W2324844435 hasRelatedWork W2288831003 @default.
- W2324844435 hasRelatedWork W2329724843 @default.
- W2324844435 hasRelatedWork W2503440624 @default.
- W2324844435 hasRelatedWork W2795644542 @default.
- W2324844435 hasRelatedWork W2810171306 @default.
- W2324844435 hasRelatedWork W2951705683 @default.
- W2324844435 hasRelatedWork W2973118323 @default.
- W2324844435 hasRelatedWork W2980428313 @default.
- W2324844435 hasRelatedWork W619930982 @default.
- W2324844435 hasRelatedWork W68468350 @default.
- W2324844435 isParatext "false" @default.
- W2324844435 isRetracted "false" @default.
- W2324844435 magId "2324844435" @default.
- W2324844435 workType "article" @default.