K-f环上格序模的张量积

Tensor Products of Lattice Ordered Modules over K f Rings

研究ｐ１Ｒｉ的由Ｒｉ（ｉ＝１，２，…，ｐ）的序所诱导的序，证明ｐ１Ｒ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Ｒ１Ｒ２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．

Let R i be K f rings, where K is a commutative lattice ordered ring with identity. We discuss the order induced on p1R i by the original order on R i and prove that p1R i is an f ring with respect to this order. Moreover piR i is an f ring with identity if R i is an f ring with identity, i=1,2,…,p . An l R 1R 2 map is introduced into the category of lattice ordered modules over K f rings where R 1 and R 2 may not equal and the tensor product 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 tensor product of M 1 and M 2 exists uniquely.