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| 幺半群的内射类及投射类刻画 | |
| 引用本文： | 闫统江,Javed Ahsan,费翔历,肖国镇.幺半群的内射类及投射类刻画[J].数学进展,2007,36(3):321-326. |
| 作者姓名： | 闫统江 Javed Ahsan 费翔历 肖国镇 |
| 作者单位： | 1. 中国石油大学数学与计算科学学院,东营,山东,257061;西安电子科技大学综合业务数据网国家重点实验室,西安,陕西,710071 2. Department of Mathematical Sciences,King Fahd University of Petroleum and Minerals,Dhahran 31261,Saudi Arabia 3. 中国石油大学数学与计算科学学院,东营,山东,257061 4. 西安电子科技大学综合业务数据网国家重点实验室,西安,陕西,710071 |
| 摘 要： | 类比于一般环上模的内射类,定义了幺半群上的S-系的内射类和投射类,并利用它们刻画了几类特殊的幺半群．证明了完全内射幺半群和完全拟内射幺半群是等价的．并且证明了对于标致幺半群S,它是完全投射的当且仅当它是完全拟投射的当且仅当它上面的投射S-系构成了一个投射类． |
| 关 键 词： | 半群 幺半群 S-系 内射类 投射类 |
| 文章编号： | 1000-0917（2007）03-0321-06 |
| 修稿时间： | 2005-11-08 |
Monoids Characterized by Their Injectivity and Projectivity Classes |
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| YAN Tongjiang,Javed Ahsan,FEI Xiaiigli,XIAO Guozhen.Monoids Characterized by Their Injectivity and Projectivity Classes[J].Advances in Mathematics,2007,36(3):321-326. | |
| Authors: | YAN Tongjiang Javed Ahsan FEI Xiaiigli XIAO Guozhen |
| Abstract: | In this paper we initiate the study of injectivity classes of S-acts over monoids, analogous to the ring theoretical notion of injectivity classes of general modules.We also in- troduce the dual notion of projectivity classes of S-acts and apply these notions to characterize certain classes of monoids.Among other results,we show that a monoid is completely injec- tive if and only if it is completely quasi-injective.Furthermore,if I is a projectivity class of S-acts over a perfect monoid S,then S is completely projective if and only if S is completely quasi-projective if and only if I is the category of right S-acts over S. |
| Keywords: | semigroup monoid S-act injectivity projectivity |
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