报 告 人：Lia Vas 教授
工作单位：University of the Sciences in Philadelphia
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.