| 可分解半群的Morita等价 |
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| 引用本文： | 陈裕群,岑嘉评.可分解半群的Morita等价[J].数学学报,2003,46(3):497-506. |
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| 作者姓名： | 陈裕群 岑嘉评 |
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| 作者单位： | 1. 华南师范大学数学系,广州,510631
2. 香港中文大学数学系,香港 |
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| 基金项目： | 国家自然科学基金(19971028)，香港UGC基金(2160092)，广东省自然科学基金(000463,021073)，高校自然科学基金(z02017)资助项目 |
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| 摘 要： | 设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构.
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| 关 键 词： | 范畴 S-系 可分解半群 Morita等价 |
| 文章编号： | 0583-1431(2003)03-0497-10 |
| 修稿时间： | 1999年8月3日 |
Morita Equivalence for Factorisable Semigroups |
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| Yu Qun CHEN.Morita Equivalence for Factorisable Semigroups[J].Acta Mathematica Sinica,2003,46(3):497-506. |
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| Authors: | Yu Qun CHEN |
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| Institution: | Yu Qun CHEN (Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China)
K. P. SHUM (Deportment of Mathematics, The Chinese University of Hong Kong, Hong Kong, P. R. China) |
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| Abstract: | Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context (S,R, sPR, RQs, <>, ) with <> and surjec-tive. For a factorisable semigroup S, we denote ζS = {(s1, s2)∈ S× S| ss1 = ss2, s ∈ S}, S' = S/ζs and U S-FAct= {SM ∈ S-Act | SM = M and SHoms(S, M)≌ M}. We show that, for factorisable semigroups S and R, the categories U S-FAct and U R-FAct are equivalent if and only if the semigroups S' and R' are strongly Morita equivalent. Some conditions for a factorisable semigroup to be strongly Morita equivalent to a sandwich semigroup, local units semigroup, monoid and group respectively are also given. Moreover, we show that a semigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I, S SHoms(S, i∈I S)→ i∈I S, s t·f → (st)f is an S-isomorphism. |
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| Keywords: | Category S-acts Factorisable semigroup Morita equivalence |
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