Matroidal hypervector spaces (Q1180136)

The author continues his earlier investigations stated in [Riv. Mat. Pura Appl. 3, 39-48 (1988; Zbl 0684.16023)] and [Rend. di Mat., Roma, to appear]. A closure system in a hypervector space is introduced, and using it the concept of matroidal hypervector space is defined to be a hypervector space with the closure operator in which the so-called exchange axiom holds. The author pays the particular attention to the investigation of the so-defined matroids. For details the reader should consult the paper itself.