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Skew-field of trace-preserving endomorphisms, of translation group in affine plane

dc.creatorZaka, Orgest
dc.creatorMohammed, Mohanad A.
dc.date2020-07-28
dc.date.accessioned2020-07-29T16:38:00Z
dc.date.available2020-07-29T16:38:00Z
dc.identifierhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4273
dc.identifier10.22199/issn.0717-6279-2020-04-0052
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/147140
dc.descriptionWe will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an affine plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of tracepreserving endomorphisms together with the actions of ’addition’ and ’composition’ (which is in the role of ’multiplication’) forms a skewfield.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.en-US
dc.relationhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4273/3468
dc.rightsCopyright (c) 2020 Orgest Zaka, Mohanad A. Mohammeden-US
dc.rightshttp://creativecommons.org/licenses/by/4.0en-US
dc.sourceProyecciones (Antofagasta, On line); Vol. 39 No. 4 (2020): Special Issue: Mathematical Computation in Combinatorics and Graph Theory; 823-850en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 39 Núm. 4 (2020): Special Issue: Mathematical Computation in Combinatorics and Graph Theory; 823-850es-ES
dc.source0717-6279
dc.source10.22199/issn.0717-6279-2020-04
dc.subjectAffine planeen-US
dc.subjectTrace-preserving endomorphismsen-US
dc.subjectTranslation groupen-US
dc.subjectSkewfielden-US
dc.subject51-XXen-US
dc.subjectGeometryen-US
dc.subject51Axxen-US
dc.subjectLinear incidence geometryen-US
dc.subject51A25en-US
dc.subjectAlgebraization in linear incidence geometryen-US
dc.subject51A40en-US
dc.subjectTranslation planes and spreads in linear incidence geometryen-US
dc.subject08Axxen-US
dc.subjectAlgebraic structuresen-US
dc.subject16-XXen-US
dc.subjectAssociative rings and algebrasen-US
dc.subject16W20en-US
dc.subjectAutomorphisms and endomorphismsen-US
dc.subject16Sxxen-US
dc.subjectAssociative rings and algebras arising under various constructionsen-US
dc.subject12E15en-US
dc.subjectSkew fields, division ringsen-US
dc.titleSkew-field of trace-preserving endomorphisms, of translation group in affine planeen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US


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