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学术报告九十一: Lia Vas — CLASSES OF ALMOST CLEAN RINGS(二)

时间:2022-09-21 作者: 点击数:

报告时间2022年9月28日(星期三)19:30-21:30

报告地点腾讯会议:138-191-532

告 人Lia Vas 教授

工作单位:University of the Sciences in Philadelphia

举办单位:数学学院

报告人简介:Lia Vas,美国费城科技大学教授、博士生导师,2002年获得美国马里兰大学博士学位,2018年为费城科技大学教授,主要研究方向为环论。在J. Algebra., J. Pure. Appl. Algebra, Comm. Algebra等杂志上发表高质量论文30余篇。

报告简介A ring is clean (almost clean) if each of its elements is the sum of a unit (regular element) and an idempotent. A module is clean (almost clean) if its endomorphism ring is clean (almost clean). We show that every quasi-continuous and nonsingular module is almost clean and that every right CS (i.e. right extending) and right nonsingular ring is almost clean. As a corollary, all right strongly semihereditary rings, including_nite AW-algebras and noetherian Leavitt path algebras in particular, are almost clean.We say that a ring R is special clean (special almost clean) if each element a can be decomposed as the sum of a unit (regular element) u and an idempotent e with aR \ eR = 0: The Camillo-Khurana Theorem characterizes unit-regular rings as special clean rings. We prove an analogous theorem for abelian Rickart rings: an abelian ring is Rickart if and only if it is special almost clean. As a corollary, we show that a right quasi-continuous and right nonsingular ring is left and right Rickart.


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