SAMS Subject Classification Number: 15

Near-vector spaces are a generalisation of vector spaces, as near-rings are a generalisation of rings. A number of authors have attempted to define the notion of a near-vector space, we will focus on André’s near-vector spaces [1]. Hyper nearrings and hyper vector spaces have been defined and studied (see [2] and [3], for example). It is thus natural to progress to the notion of a hyper near-vector space. In this talk we discuss the construction of a hyper near-vector space generalised from the hyper vector spaces defined in [2]. We obtain a space having similar properties to Johannes André’s near-vector space. We define important concepts including independence, the notion of a basis, regularity, subhyperspaces and as a highlight prove that there is a Decomposition Theorem for these spaces. This work is joint work with Prof B. Davvaz, Department of Mathematics, Yazd University, Iran.

[1] J. André, Lineare Algebra über Fastkörpern, Math. Z. 136 (1974), 295–313.

[2] M. Al Tahan and B. Davvaz, Hyper vector spaces over Krasner hyperfields, J. algebr. hyperstrucres log. algebr. 1 (3) (2020), 61–72.

[3] M. Tallini, Hyper vector spaces, Proc. of the Fourth Int. Congress on A.H.A., Greece, (2002) Spanidis Press, Xanthi, 2002.