Zhejiang Daxue xuebao. Lixue ban (Jan 2012)

Semiclean rings and their extensions(Semiclean环及其扩张)

  • GUOLi-qin(郭莉琴),
  • WANGGuo-jun(汪国军)

DOI
https://doi.org/10.3785/j.issn.1008-9497.2012.01.002
Journal volume & issue
Vol. 39, no. 1
pp. 4 – 8

Abstract

Read online

对clean环进行了推广，研究了 semiclean环，讨论了 semiclean环的几个重要性质；证明了(1)R是semi-clean 环;(2)R上的形式幂级数环R[[x]]是semiclean环；(3)R上的斜幂级数环R[[x;α]是semiclean环等价；最后证明了，如果R是环，(S，≤)是严格偏序幺半群且对任意s∈S，都有0≤s，则[[RS, ≤]]是semiclean环当且仅当R是semiclean环.

Keywords