摘要
本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．
In this paper, we defined universally the tensor product of semimodules, and constructed the direct lim rlim Ci for any directed set of indices and an arbitrary directed direct system in the category C of semimodules over a semiring R , also the cokernel of any morphism f. We discussed some properties of the tensor product of semimodules. The main results are as the following: the tensor functor preserves right exactness of semimodules and coproduct, and also coproduct preserves flatness of semimodules, the tensor functor preserves direct limits and cokernel.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2002年第1期139-150,共12页
Acta Mathematica Sinica：Chinese Series
基金
江西省自然科学基金资助项目
关键词
半模
张量积
上极限
平坦半模
同态
半环
Tensor product of semimodules
Direct limits
Flat semimodules
