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

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

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

scholarly journals Functorial radicals and non-abelian torsion

1980 ◽  
Vol 23 (3) ◽  
pp. 317-329 ◽  
Author(s):  
Shalom Feigelstock ◽  
Aaron Klein
Keyword(s):  
Nilpotent Groups ◽  
Module Theory ◽  
Abelian Categories ◽  
Torsion Theories ◽  
Nil Radical

Radicals appear in many algebraic contents. For modules over a ring, they give rise to pre-torsion and torsion theories, Goldman (5), Lambek (14). In the category of groups, Kurosh, Plotkin and others have introduced radicals (6), (13), (21), but unlike the radicals in module theory these radicals are not necessarily functorial, as for example the nil radical and the Hirsch-Plotkin radical (6). The functorial method in module theory has been extended to abelian categories, Dickson (2), to the category of nilpotent groups, Hilton (8), Warfield (25), and to the category of groups, Plotkin (22), and to general categories, Wiegandt (26), Holcombe and Walker (10).

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