| 半环上的三角矩阵乘法半群的自同构 |
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| 引用本文： | 张国勇,谭宜家,黄惠玲. 半环上的三角矩阵乘法半群的自同构[J]. 数学的实践与认识, 2009, 39(10) |
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| 作者姓名： | 张国勇 谭宜家 黄惠玲 |
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| 作者单位： | 1. 福建交通职业技术学院,基础部,福建,福州,350007
2. 福州大学,数学与计算机科学学院,福建,福州,350002 |
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| 摘 要： | 设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2.
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| 关 键 词： | 半环 矩阵代数 乘法半群 自同构 |
Multiplicative Semigroup Automorphisms of Upper Triangular Matrices over Semirings |
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| ZHANG Guo-yong,TAN Yi-jia,HUANG Hui-ling. Multiplicative Semigroup Automorphisms of Upper Triangular Matrices over Semirings[J]. Mathematics in Practice and Theory, 2009, 39(10) |
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| Authors: | ZHANG Guo-yong TAN Yi-jia HUANG Hui-ling |
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| Abstract: | Suppose R is a semiring and C the central subsemiring of R. Let Tn(R) be the C-algebra of upper triangular n×n matrices over R. In this paper, it is proved that if n≥2 and R is an effective semiring or a semiring in which all idempotents are central elements, then Φ:Tn(R)→Tn(R) is a multiplicative semigroup automorphism if and only if there exist a invertible G∈Tn(R) and a semiring automorphism τ of R such that Φ(A)=G-1τ(A)G for all A=(aij)n×n inTn(R). where τ(A)=(τ(aij))n×n. |
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| Keywords: | semiring matrix algebra multiplicative semigroup automorphism |
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