ON THE UPPER NIL RADICAL FOR R-MODULES

2019 ◽  
Vol 42 (2) ◽  
pp. 171-187
Author(s):  
N. J. Groenewald
Keyword(s):  
Nil Radical

scholarly journals A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350121 ◽  
Author(s):  
AGATA SMOKTUNOWICZ
Keyword(s):  
Jacobson Radical ◽  
Analogous Result ◽  
Graded Rings ◽  
Radical Ring ◽  
Graded Ring ◽  
Nil Ring ◽  
Nil Radical

It was shown by Bergman that the Jacobson radical of a Z-graded ring is homogeneous. This paper shows that the analogous result holds for nil radicals, namely, that the nil radical of a Z-graded ring is homogeneous. It is obvious that a subring of a nil ring is nil, but generally a subring of a Jacobson radical ring need not be a Jacobson radical ring. In this paper, it is shown that every subring which is generated by homogeneous elements in a graded Jacobson radical ring is always a Jacobson radical ring. It is also observed that a ring whose all subrings are Jacobson radical rings is nil. Some new results on graded-nil rings are also obtained.

Another characterization of the upper nil radical

2016 ◽  
Vol 150 (2) ◽  
pp. 303-311
Author(s):  
N. J. Groenewald
Keyword(s):  
Nil Radical

Köthe’s upper nil radical for modules

2013 ◽  
Vol 138 (4) ◽  
pp. 295-306 ◽  
Author(s):  
N. J. Groenewald ◽  
D. Ssevviiri
Keyword(s):  
Nil Radical

On the Levitzki nil radical

1965 ◽  
Vol 16 (1) ◽  
pp. 22-24 ◽  
Author(s):  
A. P. J. van der Walt
Keyword(s):  
Nil Radical

scholarly journals The Nil Radical for Lie or Anti-Lie Triple Systems

1993 ◽  
Vol 158 (1) ◽  
pp. 226-232 ◽  
Author(s):  
N. Kamiya
Keyword(s):  
Triple Systems ◽  
Nil Radical

The lower nil radical of (1, 1) Algebras

1985 ◽  
Vol 13 (6) ◽  
pp. 1419-1447
Author(s):  
Ng Seong Nam
Keyword(s):  
Nil Radical

Nil radical of fuzzy ideal

1992 ◽  
Vol 47 (1) ◽  
pp. 117-120 ◽  
Author(s):  
F.I. Sidky ◽  
S.A. Khatab
Keyword(s):  
Fuzzy Ideal ◽  
Nil Radical

The lower nil radical of rings of type (γ, δ)

1978 ◽  
Vol 17 (3) ◽  
pp. 199-209 ◽  
Author(s):  
A. S. Markovichev
Keyword(s):  
Nil Radical
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