| 非负半环上强保持幂零矩阵的线性算子 |
| |
| 引用本文： | 李红海,谭宜家.非负半环上强保持幂零矩阵的线性算子[J].东北数学,2007,23(1):71-86. |
| |
| 作者姓名： | 李红海 谭宜家 |
| |
| 作者单位： | Department of Mathematics University of Science and Technology of China，Hefei，230026，Department of Mathematics，Fuzhou University，Fuzhou，350002 |
| |
| 摘 要： | Let S be an antinegative commutative semiring without zero divisors and M_n(S)be the semiring of all n×n matrices over S.For a linear operator L on M_n(S),we say that L strongly preserves nilpotent matrices in M_n(S)if for any A∈M_n(S),A is nilpotent if and only if L(A)is nilpotent.In this paper,the linear operators that strongly preserve nilpotent matrices over S are characterized.
|
| 关 键 词： | 非负半环 强保持矩阵 幂零矩阵 线性算子 |
| 文章编号： | 1000-1778（2007）01-0071-16 |
| 收稿时间： | 2006-01-10 |
| 修稿时间： | 2006-01-10 |
Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings |
| |
| LI Hong-hai,TAN Yi-jia.Linear Operators That Strongly Preserve Nilpotent Matrices over Antinegative Semirings[J].Northeastern Mathematical Journal,2007,23(1):71-86. |
| |
| Authors: | LI Hong-hai TAN Yi-jia |
| |
| Abstract: | Let S be an antinegative commutative semiring without zero divisors and Mn(S) be the semiring of all n × n matrices over S. For a linear operator L on Mn(S), we say that L strongly preserves nilpotent matrices in Mn(S) if for any A ∈ Mn(S), A is nilpotent if and only if L(A) is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized. |
| |
| Keywords: | antinegative commutative semiring Boolean algebra nilpotent matrix linear operator |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
