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ON QUASI-REGULAR AND NILPOTENT ELEMENTS IN SUPERTOPOLO-GICAL NEAR-RINGS


BHASKAR VASHISHTH 1, DAVINDER SINGH 2
1. University of Delhi, Department of Mathematics, 110007 New Delhi, INDIA e-mail: abelianbhaskar@gmail.com
2. Sri Aurobindo College Department of Mathematics, University of Delhi 110007 New Delhi, INDIA e-mail: dstopology@gmail.com

Issue:

SSRSMI, Number 2, Volume XXXII

Section:

Volume 32, Number 2

Abstract:

We study supertopological near-rings in which either the set of quasi-regular element is d-open (called Q-supertopological rings) or the set of nilpotent elements is d-open. We have also characterized Q-supertopological rings among near-rings in terms of right ideals. Sev-eral properties regarding the Jacobson radical of such a supertopological ring are proved. Assuming that the set of nilpotent elements is d-open and the supertopological ring is right d-bounded, it is shown that the Jacobson radical is d-open.

Keywords:

supertopological rings, radical, supertopological near-rings, d-compact, d-bounded, D-supercontinuous.

Code [ID]:

SSRSMI202202V32S01A0007 [0005527]

Note:

DOI:

Full paper:

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