发表机构
Mälardalen University（马尔默达尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过G-左理想研究左理想整相关，刻画其交集为上幂零根，并引入左KI-环类，证明左Artin环、PI-环、代数代数及小维数代数为左KI-环，关联Köthe猜想。
AI 中文摘要
我们利用G-左理想研究左理想上的整相关，G-左理想即关于固定元素整性失败的最大左理想。我们建立了G-左理想的若干刻画，并证明其交集恰为上幂零根。受Köthe猜想的启发，我们引入左KI-环类，即固定左理想上的整左理想之和仍在该理想上整的环。证明了左Artin环、PI-环、代数代数以及维数小于基域基数的代数是左KI-环。
英文摘要
We study integral dependence over left ideals using G-left ideals, namely left ideals maximal with respect to the failure of integrality of a fixed element. We establish several characterizations of G-left ideals, and show that their intersection is precisely the upper nilradical. Motivated by the Köthe conjecture, we introduce the class of left KI-rings as rings in which sums of left ideals integral over a fixed left ideal remain integral over that ideal. It is shown that left artinian rings, PI-rings, algebraic algebras, and algebras of dimension smaller than the cardinality of the ground field are left KI-rings.
Comments23 pages
