| 幺半群的强半格上的Rees矩阵半群的平移壳 |
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| 引用本文： | 黎宏伟,周永安.幺半群的强半格上的Rees矩阵半群的平移壳[J].数学的实践与认识,2012,42(12):150-158. |
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| 作者姓名： | 黎宏伟 周永安 |
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| 作者单位： | 宿迁学院二系,江苏宿迁,223800 |
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| 基金项目： | 宿迁市项目，宿迁学院项目 |
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| 摘 要： | 设含幺元的半群A是幺半群A~_e的半格,其中A的幺元为1_A,A~_e的幺元为e,所有幺元e的集合为E(A),则对于幺半群A上的Rees矩阵半群S和幺半群A~_e上的Rees矩阵半群S~_e,以下五个条件是等价的:(1)任意的e∈E(A),a∈A,有ae=ea;(2)A是幺半群A~_e的强半格;(3)S是S~_e的强半格;(4)A的平移壳和A~_e的平移壳的强半格同构;(5)S的平移壳和S~_e的平移壳的强半格同构.
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| 关 键 词： | 平移壳 幺半群 Rees矩阵半群 半格 强半格 |
The Translational Hull of the Rees Matrix Semigroup over the Strong Semilattice of Monoids |
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| LI Hong-wei
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ZHOU Yong-an.The Translational Hull of the Rees Matrix Semigroup over the Strong Semilattice of Monoids[J].Mathematics in Practice and Theory,2012,42(12):150-158. |
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| Authors: | LI Hong-wei ZHOU Yong-an |
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| Institution: | (The Second Department,Suqian College,Suqian 223800,China) |
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| Abstract: | Let A be a monoid and A be the semilattice of monoids {A_e} with the identity of A is 1_a and the identity of A_e is e.Let E(A)be the set of all the identities e of A_e.Let S be the Rees semigroup over A and S_e be the Rees semigroup over A_e.Then the the following five conditions axe equivalent:(1)For all e∈E(A),a∈A,ae = ea;(2)A is the strong semilattice of the monoids {A_e};(3)S is the strong semilattice of {S_e};(4)The translationsl hull of A and the strong semilattice of the translational hulls of {A_e} are isomorphic;(5)The translational hull of S and the strong semilattice of the translational hulls of {S_e} are isomorphic. |
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| Keywords: | the translational hull monoid Rees matrix semigroup semilattice strong semilattice |
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