Quasi-k-normal ring
DOI:
https://doi.org/10.22199/issn.0717-6279-4849Keywords:
Abelian rings, quasi-k-normal rings, Π-regular ringsAbstract
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.
References
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
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Copyright (c) 2023 Kumar Napoleon Deka, Helen K. Saikia
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