Tensor Products of Lattice Ordered Modules over K-f Rings

Abstract:

      Let R_i be K-f rings, where K is a commutative lattice ordered ring with identity. We discuss the order induced on (?)Ｒ_ｉ by the original order on R_i and prove that (?)Ｒ_ｉ is an f ring with respect to this order. Moreover(?)Ｒ_ｉ is an f ring with identity if R_i is an f ring with identity, i=1,2,…,p . An l-R₁(?)Ｒ₂ map is introduced into the category of lattice ordered modules over K-f rings where R₁ and R₂ may not equal and the tensorp roduct of lattice ordered modules over K-f rings is defined. When M_i is a lattice ordered module over K-f ring R_i with identity, i = 1, 2 , we show that the tensorp roduct of M₁ and M₂ exists uniquely.