On matrix Lie rings over an associative commutative ring with 1 that contain the special orthogonal Lie ring

摘要

Let K be an associative and commutative ring with 1, and k a subring of K such that 1. k and the elements 2, 3 are invertible in k. Let n be an integer = 3 and Phi an invertible diagonal n by n matrix over k. In the paper, Lie subrings of the general linear Lie ring gln( K) containing the special orthogonal Lie ring son( k, Phi) are described provided that n = 4.