JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 20-24.doi: 10.6040/j.issn.1671-9352.0.2020.625

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Characterizations of uniquely clean elements

YING Zhi-ling, ZHANG Jing, HU Guo-lei, ZHOU Hua   

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, Jiangsu, China
  • Published:2021-04-13

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Abstract: An element of a ring is called uniquely clean if it is uniquely the sum of an idempotent and a unit. An element a in a ring R is said to be left uniquely exchange if there exists a uniquely idempotent e∈R such that e∈Ra and 1-e∈R(1-a). If every idempotent of a ring R is in the center, then a∈R is uniquely clean iff a is left uniquely exchange. A characterization of uniquely clean elements in a commutative ring endowed with the Zariski topology is also given.

Key words: uniquely clean element(ring), uniquely exchange element(ring), Zariski topology

CLC Number: 

  • O153.3
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