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A note on upper nilradicals and one-sided nil ideals

Abstract

It is not known whether or not every non-zero one-sided nil ideal of a noncommutative ring is contained in the upper nilradical of the ring. Here we give necessary and sufficient conditions under which a non-zero one-sided nil ideal of a noncommutative ring is not contained in the upper nilradical of the ring.

2020 Mathematics Subject Classification:

16D99, 16N40

Keywords

ring, nil ideal, one-sided nil ideal, Jacobson radical, Koethe conjecture, upper nilradical

Full text

Author Details

Santosh Kumar Pandey

Faculty of Science, Technology and Forensic
Sardar Patel University of Police, Security and Criminal Justice
Jodhpur, India
e-mail: skpandey12@gmail.com


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