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

Omid Reza Dehghan, Morteza Norouzi and Irina Cristea
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Omid Reza Dehghan: Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord 94531, Iran
Morteza Norouzi: Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord 94531, Iran
Irina Cristea: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia

Mathematics, 2021, vol. 9, issue 18, 1-9

Abstract: 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.

Keywords: composition vector space; foundation; strong composition subspace; composition linear transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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