JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 84-90.doi: 10.6040/j.issn.1671-9352.0.2022.637

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A kind of generalization of fine rings

Yuru CUI(),Yang CHENG   

  1. College of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
  • Received:2022-11-24 Online:2024-06-20 Published:2024-06-17

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Abstract:

A ring R is fine if every nonzero element of R is the sum of a unit and a nilpotent. We introduce the concept of J#-fine rings as a generalization of fine rings, and study basic properties of J#-fine rings and the relationship between J#-fine rings and rings which associate with J#-fine rings. We discuss the J#-fineness of matrix expansion and prove that any matrix rings over J#-fine rings are J#-fine.

Key words: fine ring, J#-fine ring, matrix ring

CLC Number: 

  • O153.3
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