| 半模的张量积 |
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| 引用本文： | 陈培慈,周嫒兰. 半模的张量积[J]. 数学学报, 2002, 45(1): 139-150. DOI: cnki:ISSN:0583-1431.0.2002-01-016 |
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| 作者姓名： | 陈培慈 周嫒兰 |
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| 作者单位： | 江西师范大学数学系,江西,南昌,330027 |
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| 基金项目： | 江西省自然科学基金资助项目 |
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| 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．
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| 关 键 词： | 半模的张量积 上极限 平坦半模 |
| 文章编号： | 0583-1431(2002)01-0139-12 |
| 修稿时间： | 1999-05-17 |
Tensor Product of Semimodules |
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| CHEN Pei Ci,ZHOU Yuan Lan. Tensor Product of Semimodules[J]. Acta Mathematica Sinica, 2002, 45(1): 139-150. DOI: cnki:ISSN:0583-1431.0.2002-01-016 |
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| Authors: | CHEN Pei Ci ZHOU Yuan Lan |
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| Affiliation: | CHEN Pei Ci, ZHOU Yuan Lan (Department of Mathematics, Jiangxi Normal University, Nanchang 330027 , P. R. China ) ( E-mail: chenpeic@jxnu.cn) |
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| Abstract: | 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. |
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| Keywords: | Tensor product of semimodules Direct limits Flat semimodules |
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