非负半环上强保持幂零矩阵的线性算子

• 作 者: 李红海 谭宜家
• 机 构: Department of Mathematics, University of Science and Technology of China, Hefei, 230026Department of
• 出 处: 东北数学（英文版）
• 发表日期: 2007年1期
• 关键词: antinegative commutative semiring Boolean algebra nilpotent matrix linear operat

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.