一类l-半群的自同构

Automorphisms of a Class of l-semigroup

设R有1的全序环.记P为R的正锥,U(P)为P中所有可逆元素组成的集合.记Mn(R)为R上n×n矩阵乘法半群,则Mn(R)在通常格序下成为l-半群.引入了l-半群的∧-自同构的概念.当U(P)P时,刻画了l-半群Mn(R)的∧-自同构.

Let R be a totally ordered ring with 1, P the positive cone of R, U （P） the set consisting of all invertible elements in P. Let Mn （R） be the multiplicative semigroup consisting of all matrices over R, then it is an l -semigroup with the usual lattice order. The notion of ∧ -automorphisms of a l -semigroup is introduced, and the ∧ -automorphisms of l -semigroup Mn（R） is described when U（P）P.