대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권1호
  • /
  • Pages.83-91
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  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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UN RINGS AND GROUP RINGS

  • Kanchan, Jangra (Department of Applied Mathematics Delhi Technological University) ;
  • Dinesh, Udar (Department of Applied Mathematics Delhi Technological University)
  • 투고 : 2021.12.21
  • 심사 : 2022.05.02
  • 발행 : 2023.01.31
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초록

A ring R is called a UN ring if every non unit of it can be written as product of a unit and a nilpotent element. We obtain results about lifting of conjugate idempotents and unit regular elements modulo an ideal I of a UN ring R. Matrix rings over UN rings are discussed and it is obtained that for a commutative ring R, a matrix ring Mn(R) is UN if and only if R is UN. Lastly, UN group rings are investigated and we obtain the conditions on a group G and a field K for the group algebra KG to be UN. Then we extend the results obtained for KG to the group ring RG over a ring R (which may not necessarily be a field).

키워드

과제정보

The authors are grateful to the referee for his/her careful reading of the manuscript.

참고문헌

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