The lower nil radical in Jordan algebras with maximum condition

1977 ◽  
Vol 16 (1) ◽  
pp. 68-69 ◽  
Author(s):  
A. M. Slin'ko
Keyword(s):  
Jordan Algebras ◽  
Maximum Condition ◽  
Nil Radical

Reducibly free nonspecial Jordan algebras

1989 ◽  
Vol 30 (1) ◽  
pp. 159-160 ◽  
Author(s):  
S. R. Sverchkov
Keyword(s):  
Jordan Algebras

Multiplicative-Semiprimeness of Nondegenerate Jordan Algebras

2004 ◽  
Vol 32 (10) ◽  
pp. 3995-4003 ◽  
Author(s):  
M. Cabrera ◽  
A. R. Villena
Keyword(s):  
Jordan Algebras

scholarly journals Some inertia theorems in Euclidean Jordan algebras

2009 ◽  
Vol 430 (8-9) ◽  
pp. 1992-2011 ◽  
Author(s):  
M. Seetharama Gowda ◽  
Jiyuan Tao ◽  
Melania Moldovan
Keyword(s):  
Jordan Algebras ◽  
Euclidean Jordan Algebras

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.

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