@article { author = {Zangiabadi, Elham and Nazari, Zohreh}, title = {Convex, balanced and absorbing subsets of hypervector spaces}, journal = {Algebraic Structures and Their Applications}, volume = {7}, number = {1}, pages = {117-125}, year = {2020}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2020.1735}, 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 = {Absorbing set,Balanced set,Convex set,Hypervector space}, url = {https://as.yazd.ac.ir/article_1735.html}, eprint = {https://as.yazd.ac.ir/article_1735_97f0c335d981a14177b59c2ae16bbf39.pdf} }