Quasi-k-normal ring


  • Kumar Napoleon Deka Gauhati University.
  • Helen K. Saikia Gauhati University,




Abelian rings, quasi-k-normal rings, Π-regular rings


In [4] Wei and Libin defined Quasi normal ring. In this paper we attempt to define Quasi-k-normal ring by using the action of k-potent element. A ring is called Quasi-k-normal ring if ae = 0 ⇒ eaRe = 0 for a ∈ N(R)and e ∈ K(R), where K(R) = {e ∈ R|ek = e}. Several analogous results give in [4] is defined here. we find here that a ring is quasi-k-normal if and only if eR(1 − ek−1)Re = 0 for each e ∈ K(R). Also we get a ring is quasi-k-normal ring if and only if Tn(R, R) is quasi-k-normal ring.

Author Biographies

Kumar Napoleon Deka, Gauhati University.

Research Scholar, Department of Mathematics.

Helen K. Saikia, Gauhati University,

Professor, Department of Mathematics.


J. Han, Y. Lee and S. Park, “Structure of abelian rings”, Frontiers of Mathematics in China, vol. 12, pp. 117-134, 2016. https://doi.org/10.1007/s11464-016-0586-z

D. Mosi, “Characterizations of k-potent elements in rings”, Annali di Matematica Pura ed Applicata, vol. 194, pp. 1157-1168, 2014. https://doi.org/10.1007/s10231-014-0415-5

M. M. Parmenter and P. N. Stewart, “Normal rings and local ideals”, Mathematica Scandinavica, vol. 60, 1987.

J. Wei and L. Li, “Quasi-normal rings”, Communications in Algebra, vol. 38, no. 5, pp. 1855-1868, 2010. https://doi.org/10.1080/00927871003703943



How to Cite

K. N. Deka and H. K. . Saikia, “Quasi-k-normal ring”, Proyecciones (Antofagasta, On line), vol. 42, no. 3, pp. 599-608, May 2023.