Hyper vector spaces over Krasner hyperfields

Document Type : Original Article


1 Department of Mathematics, Lebanese International University, Bekaa, CZ-961, Lebanon

2 Department of Mathematics Yazd University, Yazd Iran


In this paper, we study hyper vector spaces over Krasner hyperfields. First, we introduce the notions of linearly independence (dependence) and basis for a hyper vector space. Second, we investigate their properties and prove some results for hyper vector spaces that are similar to that of vector spaces over fields. Then, we define linear transformations over hyper vector spaces and investigate their properties. Finally, we prove the dimension theorem for linear transformations.