【摘要】 称环R的元有强二和性质,如果它可以写成环中两个可交换单位的和.如果环R的每个元都有强二和性质,则称环R为强二和环.本文研究了3×3阶矩阵环的两个子环L(R)和■(R)的强二和性质.证明了对一交换局部环R,L(R)是强二和环当且仅当R是强二和环当且仅当■(R)是强二和环.同时还证明了对一交换局部环R,它是强二和环当且仅当T_n(R)(n=2,3)的每个角环都是强二和环.更多还原

【Abstract】 An element of a ring R is called to have the strong 2-surn property if it, is a sum of two units that commute with each other. And a ring R is called a strong 2-sum ring if every element of R has the strong 2-sum property. In this paper, we investigate the strong2-sum property of two subrings, L(R) and■(R), of 3 × 3 matrix rings over commutative local rings. We prove that for a commutative local ring R, L(R) is a strong 2-sum ring if and only if R is a strong 2-sum ring if and only if ■(R) is a strong 2-sum ring. Moreover, we prove that for a commutative local ring R, it is a strong 2-sum ring if and only if every corner ring of T_n(R)(n=2,3) is a strong 2-sum ring.更多还原