Constructions of new q-cryptomorphisms

In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which described as matroid cryptomorphisms . A q -matroid is -analogue where subspaces play role subsets in theory. this article we establish -matroids. doing so highlight difference between and its -analogue. We introduce comprehensive set axiom show them existing -matroid. These axioms rank, closure, basis, independence, dependence, circuit, hyperplane , flat, open space, spanning non-spanning bi-colouring axioms.