Strongly Transitive Geometric Spaces Associated with (m, n)-Ary Hypermodules

Abstract

Abstract In this paper, we define the strongly compatible relation ϵ on the (m, n)- ary hypermodule M, so that the quotient (M/ϵ*, h/ϵ*) is an (m, n)-ary module over the fundamental (m, n)-ary ring (R/Γ∗, f/Γ∗, g/Γ∗). Also, we determine a family P(M) of subsets of an (m, n)-ary hypermodule M and we give a sufficient condition such that the geometric space (M, P(M)) is strongly transitive.