1,000
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Bounds for the number of idempotents in finite rings

Pages 4800-4807 | Received 24 Mar 2021, Accepted 09 May 2021, Published online: 28 May 2021

References

  • Anh, P. N., Birkenmeier, G. F., van Wyk, L. (2016). Idempotents and structures of rings. Linear Multilinear Algebra 64(10):2002–2029. DOI: 10.1080/03081087.2015.1134429.
  • Anh, P. N., Birkenmeier, G. F., van Wyk, L. (2020). Peirce decompositions, idempotents and rings. J. Algebra 564:247–275. DOI: 10.1016/j.jalgebra.2020.08.003.
  • Camillo, V. P., Yu, H.-P. (1995). Stable range one for rings with many idempotents. Trans. Amer. Math. Soc. 347(8):3141–3147. DOI: 10.1090/S0002-9947-1995-1277100-2.
  • Chen, H. (1999). Rings with many idempotents. Int. J. Math Math. Sci. 22(3):547–558. DOI: 10.1155/S0161171299225471.
  • Cheraghpour, H., Ghosseiri, N. M. (2019). On the idempotents, nilpotents, units and zero-divisors of finite rings. Linear and Multilinear Algebra 67(2):327–336. DOI: 10.1080/03081087.2017.1418826.
  • Chin, A. Y. M. (2018). Finite rings of odd order with few nilpotent and idempotent elements. Amer. Math. Monthly 125(6):545–548. DOI: 10.1080/00029890.2018.1449541.
  • Dixon, J. D. (1973). Problems in Group Theory, 2nd ed. New York (NY): Dover publication, Inc.
  • Dube, T., Ghirati, M., Nazari, S., Taherifar, A. (2020). Rings in which idempotents generate maximal or minimal ideals. Algebra Univ. DOI: 10.1007/s00012-020-00660-y.
  • Kanwar, P., Khatkar, M., Sharma, R. K. (2017). Idempotents and units of matrix rings over polynomial rings. Int. Electr. J. Algebra 22:147–169.
  • MacHale, D. (1982). Idempotents in finite rings. Proc. R. Ir. Acad. 82A(1):9–12.
  • McDonald, B. R. (1974). Finite Rings with Identity, Pure and Applied Mathematics, Vol. 28. New York: Marcel Dekker, Inc., ix + p. 429 pp.
  • Mittal, G., Singla, K. (2018). On the properties of idempotents of the matrix ring M3(Zn[x]). Int. J. Math. Trends Technol. (IJMTT). 53(4):254–258.
  • Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229:269–278. DOI: 10.1090/S0002-9947-1977-0439876-2.
  • Steger, A. (1966). Diagonability of idempotent matrices. Pacific J. Math. 19(3):535–542. DOI: 10.2140/pjm.1966.19.535.
  • Weiss, A. (1980). Idempotents in group rings. J. Pure Appl. Algebra 16(2):207–213. DOI: 10.1016/0022-4049(80)90017-1.