【摘要】 文献讨论了n-扭自由(或幂零元,或换位子是n-扭自由)的s-单式环的交换性,而文献中的某些结论(定理3)推广了文献中的结果。本文则对此课题继续进行讨论,得到了比文献与中的一些结论更为广泛的结果,同时还得到了一些新的结果。更多还原

【Abstract】 In this paper following result is proved:Let R be an s-unital ring, m and n two positive integers, g be L.C.M. of m and n, then R is commutative, if commulators of R are g-torsion-free, R satisfies polynomiat indentity [x^m,yⁿ]=0, and any one of the following conditions:（1） R satisfies （xy）ⁿ⁺¹=xⁿ⁺¹yⁿ⁺¹;（1’） R satisfies （xy）^m+1=x^m+1y^m+1;（2） R satisfies [（xy）²-x²y²,x]=0;（3） Each pair x,y∈R satisfies one of the following equations: where k; is a positive integer and （k_i,n）=1;（3’） Each pair x,y∈R satisfies one of the following equations: where I_j is a positive integer and （I_i,m）=1;（4’） Each pair x,y∈R satisfies one of the following equations: where l_i and k_i are positive integers, and for every i, or,or,or;（5’） Let d be a positive integer, d|_g and each pair x,y∈R satisfies one of the following equations: where l_I,k_i are positive integers and for every i,or.or.更多还原