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| 分次Morita对偶，Morita对偶与Smash积 | |
| 引用本文： | 张圣贵. 分次Morita对偶，Morita对偶与Smash积[J]. 数学学报, 1994, 37(6): 756-761. DOI: cnki:ISSN:05831431.0.1994-06-004 |
| 作者姓名： | 张圣贵 |
| 作者单位： | 福建师范大学数学系 |
| 摘 要： | 设Ｃ和ｒ都是群，是Ｇ－型分次环，是Γ－型分次环．是双分次模，Ｒ＃Ｇ是Ｒ的Ｓｍａｓｈ积，Ａ＃Γ是Ａ的Ｓｍａｓｈ积。令Ｗ＝（＿ｇＵ＿（σ－１））＿（ｇ，σ）即（ｇ，σ）位置取＿ｇＵ＿（σ－１）的元素的｜Ｇ｜×｜Γ｜矩阵的全体组成的集合，且每个矩阵的每行和每列的非零元只有有限个，按矩阵运算，Ｗ构成（Ｒ＃６，Ａ＃Γ）双模。则＿ＲＵ＿Ａ定义了一个分次Ｍｏｒｉｔａ对偶当且仅当＿（Ｒ＃Ｇ）Ｗ＿（Ａ＃Γ）定义了一个Ｍｏｒｉｔａ对偶。 |
| 关 键 词： | 分次Morita对偶，，Morita对偶，Smash积 |
| 收稿时间： | 1992-02-09 |
Graded Morita Dualities,Morita Kualities and Smash Products |
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| zhang Shenggui. Graded Morita Dualities,Morita Kualities and Smash Products[J]. Acta Mathematica Sinica, 1994, 37(6): 756-761. DOI: cnki:ISSN:05831431.0.1994-06-004 | |
| Authors: | zhang Shenggui |
| Affiliation: | zhang Shenggui(Department of Mathematics,Fujan Normal University,Fuzhou 350007,China ) |
| Abstract: | Let G and Γ be groups,a graded ring of type G with an identity, a graded ring of type Γ with an identity,R#G and A#Γsmash products of R and A, respectively. Let W=(_gU_(σ-1))_(g,σ)i.e. a set of all|G|》×|Γ| matrices whose element in the(g,σ)-position belongs to gU_(σ-1). Suppose each matrix in W only has finitely non zero elements.Then W is an(R#G,A#Γ)-bimodule with the matrix addition and multiplication and _RU_Adefines a graded Morita duality iff _(R#G)W_(A#Γ) defines a Morita duality. |
| Keywords: | grad ed Morita duality Morita duality Smash products |
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