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

Abstract: We 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...

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Autores principales:	Zaka,Orgest, Mohammed,Mohanad A.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Affine plane Endomorphisms Trace-preserving endomorphisms Translation group Skew-field
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400835
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spelling	oai:scielo:S0716-091720200004008352020-08-13Skew-field of trace-preserving endomorphisms, of translation group in affine planeZaka,OrgestMohammed,Mohanad A. Affine plane Endomorphisms Trace-preserving endomorphisms Translation group Skew-field Abstract: We 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.4 20202020-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400835en10.22199/issn.0717-6279-2020-04-0052
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Affine plane Endomorphisms Trace-preserving endomorphisms Translation group Skew-field
spellingShingle	Affine plane Endomorphisms Trace-preserving endomorphisms Translation group Skew-field Zaka,Orgest Mohammed,Mohanad A. Skew-field of trace-preserving endomorphisms, of translation group in affine plane
description	Abstract: We 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.
author	Zaka,Orgest Mohammed,Mohanad A.
author_facet	Zaka,Orgest Mohammed,Mohanad A.
author_sort	Zaka,Orgest
title	Skew-field of trace-preserving endomorphisms, of translation group in affine plane
title_short	Skew-field of trace-preserving endomorphisms, of translation group in affine plane
title_full	Skew-field of trace-preserving endomorphisms, of translation group in affine plane
title_fullStr	Skew-field of trace-preserving endomorphisms, of translation group in affine plane
title_full_unstemmed	Skew-field of trace-preserving endomorphisms, of translation group in affine plane
title_sort	skew-field of trace-preserving endomorphisms, of translation group in affine plane
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000400835
work_keys_str_mv	AT zakaorgest skewfieldoftracepreservingendomorphismsoftranslationgroupinaffineplane AT mohammedmohanada skewfieldoftracepreservingendomorphismsoftranslationgroupinaffineplane
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Skew-field of trace-preserving endomorphisms, of translation group in affine plane

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