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
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.
