Wolfson and Xu Yonghua both discussed the abstract characterizations of full linear transformation rings and obtained two necessary and sufficient conditions for an abstract ring to be isomorphic to a full linear tran...
Let (E, F, <., .>) be dual vector spaces. A multiplication can be defined on the tensor product E(?)F as follows. By setting (x(?)u) (y(?)v)=x(?)v for x,y∈and u, v ∈F, and using the distribution law, it can be...
Ⅰ. INTRODUCTION In this paper, all the linear spaces mean left spaces. Let Ωi be the complete ring of linear transformations of a linear space (?)i over a division ring △i(i = 1, 2).in [1, Theorem 1.4.1], Xu Yo...
The structure theorem of the primitive rings with non-zero socles has been proved in Refs. [1] and (2)In the former, the finite topological method is used; and in the latter the method of right and left double modules...