共查询到18条相似文献,搜索用时 78 毫秒
1.
2.
3.
4.
设R是一个环,其上的理想包含图,记为Γ_I(R),是一个有向图,它以R的非平凡左理想为顶点,从R的左理想I_1到I_2有一条有向边当且仅当I_1真包含于I_2.环R上的理想关系图,记为Γ_i(R),也是一个有向图,它以R为顶点集,从R中元素A到B有一条有向边当且仅当A生成的左理想真包含于B生成的左理想.设F_q为有限域,其上n阶全矩阵环记为M_n(F_q),本文刻画了环M_n(F_q)上的理想包含图以及理想关系图的任意自同构. 相似文献
5.
文中研究了Γ-环M与其矩阵环Γn,m-环Mm,n根的关系,得到了:QN(Mm,n)(?)(QN(M))m,n;K(Mm,n)(?)(K(M))m,n.这里QN-根是Γ-环元素的强幂零性所确定的根,K-根是诣零根 相似文献
6.
全矩阵环的一类基 总被引:3,自引:0,他引:3
胡付高 《数学的实践与认识》2007,37(10):188-191
设P是一个域,Fij(i,j=1,2,…,n)是全矩阵环Mn(P)中n2个n×n矩阵,且满足FijFkl=δjkFil(i,j,k,l=1,2,…,n),其中δij={1,i=j0,i≠j为Kronecker符号.则或者所有Fij(i,j=1,2,…,n)全为零,或者存在可逆矩阵T∈Mn(P),使得Fij=T-1EijT(i,j=1,2,…,n),其中Eij表示(i,j)位置是1, 相似文献
7.
8.
9.
10.
11.
12.
Let R be a commutative ring with identity, Nn(R) the matrix algebra consisting of all n × n strictly upper triangular matrices over R. Several types of proper local derivations of Nn(R) (n ≤ 4) are constructed, based on which all local derivations of Nn(R) (n ≤ 4) are characterized when R is a domain. 相似文献
14.
P. A. Krylov 《Algebra and Logic》2004,43(1):34-43
The Jacobson radical of an endomorphism ring is computed for a completely decomposable torsion-free Abelian group and for a mixed Abelian group in one class of mixed groups. For the latter case, we also look into the question when a factor ring w.r.t. the radical is regular in the sense of Nuemann. 相似文献
15.
Pseudopolar rings are closely related to strongly π-regular rings, uniquely strongly clean rings and semiregular rings. In this paper, we investigate pseudopolarity of generalized matrix rings K s(R) over a local ring R. We determine the conditions under which elements of K s(R) are pseudopolar. Assume that R is a local ring. It is shown that A ∈ K s(R) is pseudopolar if and only if A is invertible or A2∈ J(K s(R)) or A is similar to a diagonal matrix[u 00 j], where l u-r j and l j-r u are injective and u ∈ U(R) and j ∈ J(R). Furthermore, several equivalent conditions for K s(R)over a local ring R to be pseudopolar are obtained. 相似文献
16.
Throughout,RisaJacobsonradicalring,anddefinea b =a +b -aband [a ,b] =ab-baforanya ,b∈R .Then (R , )isagroupwithidentity 0 ,calledtheadjointorcirclegroupofR ,and (R ,+,[,] )isaLiering ,calledtheassociatedLieringofR .ItwasprovedbyJennings[1]that(R , )isanilpotentgroupifandonlyif (… 相似文献
17.
18.
Abstract: In this paper, we consider the Goldbach's problem for matrix rings, namely, we decompose an n ×n (n > 1) matrix over a principal ideal domain R into a sum of two matrices in Mn(R) with given determinants. We prove the following result: Let n > 1 be a natural number and A = (αij) be a matrix in Mn(R). Define d(A) := g.c.d{αij}. Suppose that p and q are two elements in R. Then (1) If n > 1 is even, then A can be written as a sum of two matrices X, Y in Mn(R) with det(X) = p and det(Y) = q if and only if d(A) |p-q; (2) If n > 1 is odd, then A can be written as a sum of two matrices X, Y in Mn(R) with det(X) = p and det(Y) = q if and only if d(A) |p + q. We apply the result to the matrices in Mn(Z) and Mn(Q[x]) and prove that if R = Z or Q[x], then any nonzero matrix A in Mn(R) can be written as a sum of two matrices in Mn(R) with prime determinants. 相似文献