周伟.K-f环上格序模的张量积[J].数学研究及应用,1996,16(3):441~444 |
K-f环上格序模的张量积 |
Tensor Products of Lattice Ordered Modules over K-f Rings |
投稿时间:1993-11-24 |
DOI:10.3770/j.issn:1000-341X.1996.03.027 |
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. |
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中文摘要: |
研究(?)Ri的由Ri(i=1,2,…,p)的序所诱导的序,证明(?)Ri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 Ri be K-f rings, where K is a commutative lattice ordered ring with identity. We discuss the order induced on (?)Ri by the original order on Ri and prove that (?)Ri is an f ring with respect to this order. Moreover(?)Ri is an f ring with identity if Ri 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 Mi is a lattice ordered module over K-f ring Ri with identity, i = 1, 2 , we show that the tensorp roduct of M1 and M2 exists uniquely. |
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