Composition Vector Spaces as a New Type of Tri-Operational Algebras

The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operat...

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Main Authors:	Omid Reza Dehghan, Morteza Norouzi, Irina Cristea
Format:	Article
Language:	English
Published:	MDPI AG 2021-09-01
Series:	Mathematics
Subjects:	composition vector space foundation strong composition subspace composition linear transformation
Online Access:	https://www.mdpi.com/2227-7390/9/18/2344

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spelling	doaj-edc6b879d9ed4226b7a7b75ac1d5a6c02021-09-26T00:38:46ZengMDPI AGMathematics2227-73902021-09-0192344234410.3390/math9182344Composition Vector Spaces as a New Type of Tri-Operational AlgebrasOmid Reza Dehghan0Morteza Norouzi1Irina Cristea2Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord 94531, IranDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord 94531, IranCentre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, SloveniaThe aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations.https://www.mdpi.com/2227-7390/9/18/2344composition vector spacefoundationstrong composition subspacecomposition linear transformation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Omid Reza Dehghan Morteza Norouzi Irina Cristea
spellingShingle	Omid Reza Dehghan Morteza Norouzi Irina Cristea Composition Vector Spaces as a New Type of Tri-Operational Algebras Mathematics composition vector space foundation strong composition subspace composition linear transformation
author_facet	Omid Reza Dehghan Morteza Norouzi Irina Cristea
author_sort	Omid Reza Dehghan
title	Composition Vector Spaces as a New Type of Tri-Operational Algebras
title_short	Composition Vector Spaces as a New Type of Tri-Operational Algebras
title_full	Composition Vector Spaces as a New Type of Tri-Operational Algebras
title_fullStr	Composition Vector Spaces as a New Type of Tri-Operational Algebras
title_full_unstemmed	Composition Vector Spaces as a New Type of Tri-Operational Algebras
title_sort	composition vector spaces as a new type of tri-operational algebras
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2021-09-01
description	The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations.
topic	composition vector space foundation strong composition subspace composition linear transformation
url	https://www.mdpi.com/2227-7390/9/18/2344
work_keys_str_mv	AT omidrezadehghan compositionvectorspacesasanewtypeoftrioperationalalgebras AT mortezanorouzi compositionvectorspacesasanewtypeoftrioperationalalgebras AT irinacristea compositionvectorspacesasanewtypeoftrioperationalalgebras
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Composition Vector Spaces as a New Type of Tri-Operational Algebras

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