On weakly nil-clean rings

Kosan M. T., Zhou Y.

FRONTIERS OF MATHEMATICS IN CHINA, cilt.11, sa.4, ss.949-955, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 4
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s11464-016-0555-6
  • Dergi Adı: FRONTIERS OF MATHEMATICS IN CHINA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.949-955
  • Gazi Üniversitesi Adresli: Hayır

Özet

We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring M-n(R) is weakly nil-clean, and to show that the endomorphism ring End(D)(V) over a vector space V-D is weakly nil-clean if and only if it is nil-clean or dim(V) = 1 with D congruent to Z(3).