数学与统计学院知识库

令(BU_n,*)是主对角线上元素全为1的布尔矩阵在矩阵乘法和次对角线转置运算下构成的对合半群,本论文研究了其有限基问题,证明了对合半群(B U_3,*)是有限基的,同时给出它的一组有限基;证明了对合半群(BU_n,*)(n≥5)是非有限基的;给出了对合半群(BU_4,*)满足的一些等式及其性质,从而部分地回答了Auinger等人提出的一个公开问题。

We study the finite bases problem for involution semigroups(BU_n,*) of all boolean upper triangular nxn matrices with 1's on the main diagonal (The unary operation is reflection with respect to the secondary diagonal).In this paper,it is shown that the involution monoid (BU_3,*) is finitely based,and a finite identity for the involution monoid (BU_3,*) is given;it is shown that the involution monoid (BU_n,*) is nonfinitely based when  n≥5.Some identities and properties it satisfied are given.