Convex, balanced and absorbing subsets of hypervector spaces

Document Type : Research Paper

Authors

Department of Mathematics, Vali-e-Asr University of Rafsanjan, P. O. Box 7713936417, Rafsanjan, Iran

Abstract

In this paper, we define convex, balanced and absorbing subsets of a hypervector space $V$ over a field $K$, where $K$ is considered $\mathbb{R}$ or $\mathbb{C}$ and give some examples of them. We prove that every subspace of a hypervector space is a convex and balanced subset. Also, for every regular equivalence relation $\rho$ on a hypervector space $V$, we  show that if $A$ is a convex, balanced or an absorbing subset of $V$, then $A/\rho$ is respectively a convex, balanced or an absorbing subset of a hypervector space $V/\rho$.

Keywords

References

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Algebraic Structures and Their Applications
Volume 7, Issue 1
February 2020
Pages 117-125

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