PRIME RINGS WITH FINITENESS PROPERTIES ON ONE-SIDED IDEALS

Proceedings of the Edinburgh Mathematical Society

Tsiu-Kwen Lee¹ 

关键词: prime ring;    polynomial identity (PI);    generalized polynomial identity (GPI);    extended centroid;   

DOI  :  10.1017/S0013091501000050

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let R be a prime ring with extended centroid C, $ho$ a non-zero right ideal of R and let $f(X_1,dots,X_t)$ be a polynomial, having no constant term, over C. Suppose that $f(X_1,dots,X_t)$ is not central-valued on RC. We denote by $f(ho)$ the additive subgroup of RC> generated by all elements $f(x_1,dots,x_t)$ for $x_iinho$. The main goals of this note are to prove two results concerning the extension properties of finiteness conditions as follows.(I) If $f(ho)$ spans a non-zero finite-dimensional $C$-subspace of $RC$, then $dim_CRC$ is finite.(II) If $f(ho)e0$ and is a finite set, then $R$ itself is a finite ring.AMS 2000 Mathematics subject classification: Primary 16N60; 16R50

【 授权许可】

Unknown