构造矩阵环中的超幂零根  

ON THE SUPERNILPONENT RADICAL IN THE STRUCTURAL MATRIX RINGS

作　　者：王吉安[1] 

机构地区：[1]益阳师专

出　　处：《益阳师专学报》1994年第6期12-16,共5页Journal of Yiyang Teachers College

摘　　要：本文首先是讨论在一个环T上全阵环的超幂零根。然后本文的主要目的是研究构造矩阵环──Mn（T）的子环的超幂零根。结果表明对于只要S有单位元满足S∈K当且有仅当Mn（S）∈K的弱特别环类K所确定的超幂零根R，那么（i）R（Mn（T）＝Mn（R（T））；（ii）对由一个nxn布尔矩阵B所决定的构造矩阵环S（B，T），R［S（B，T）］是二理想之和，即为S［B，R（T）］与B的逆对称部分中取自T中元的所有矩阵的集之和。This paper is first meant to the discuss supernilpotent radicals of the complete matrix ring Mn(T)overa ring T. Then the main purpose of this paper is to study supernilpotent radicals of structural matrixring,i. e.subrings of Mn(T). The results show that for a supernilpotent radical R determinded by awenkly special class K of rings such tha s∈K iff Mn(s) ∈K whenever S has an identify and everyring T,then. (I ) IR (Mn(T)) = Mn[R(T)] (Ⅱ)for the structural matrix ing S(B.T) determined byan nxn Boolean matrix B,R[S(B,T)] is the sum of two ideals, namely S[B,R(T)] and set of allmatrices with eatries from T in the 'antisymmetric part'of B.

关 键 词：构造矩阵环 半素理想 超幂零限 子环 

分 类 号：O153.3[理学—数学]