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...
Acknowledgements The author was grateful to the referees for their detailed reading and helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 11201269), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and the Young Scholars Research Fund of Shandong University of Technology.
We investigate the properties of nil-Coxeter algebras and nil-Ariki- Koike algebras. To be precise, from the view of standardly based algebras introduced by J. Du, H. Rui [Trans. Amer. Math. Soe, 1998, 350: 3207-3235...