This paper extends Hua's theorem on the geometry of rectangular matrices over a division ring to the case of Bezout domains. Let m,n, m′, n′ be integers ≥2, R an R′ be two Bezout domains. Assume that :Rm× n→R′m′× n′ is an adjacency preserving bijective map in both directions. Further, assume that R′ is a local ring, or is an invertibility preserving map, or is an additive map. This paper obtains the algebraic formulas of . As applications, the ring semi-isomorphisms from Rm× n to R′ m′× n′ are characterized, and the group isomor...
