K-f环上格序模的张量积

Tensor Products of Lattice Ordered Modules over K-f Rings

中文关键词:  K-f环  格序模  张量积．

英文关键词:K-f rings  lattice ordered modules  tensor product.

中文摘要:

      研究(?)Ｒ_ｉ的由Ｒ_ｉ（ｉ＝１，２，…，ｐ）的序所诱导的序，证明(?)Ｒ_ｉ在一定条件下作成一个有单位元的ｆ环，并在有单位元的Ｋ-ｆ环上的格序模范畴中引入保格Ｒ₁(?)Ｒ₂映射，进一步定义了张量积，使张量积概念在不同序环的序模范畴得到拓展．

英文摘要:

      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.