scholarly journals The Jacobson radical of monoid-graded algebras

1992 ◽  
Vol 16 (1) ◽  
pp. 19-52 ◽  
Author(s):  
G. Karpilovsky
Keyword(s):  
Jacobson Radical ◽  
Graded Algebras

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

2020 ◽  
Vol 32 (6) ◽  
pp. 1395-1406
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Loop Spaces ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Algebraic Description ◽  
Acyclic Map ◽  
Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

scholarly journals Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Ravi Srinivasa Rao ◽  
K. Siva Prasad ◽  
T. Srinivas
Keyword(s):  
Jacobson Radical ◽  
Paper Properties ◽  
Hereditary Radical ◽  
Constant Part ◽  
The Right

By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.

Simultaneous Triangularization of Algebras of Polynomially Compact Operators

1991 ◽  
Vol 34 (2) ◽  
pp. 260-264 ◽  
Author(s):  
M. Radjabalipour
Keyword(s):  
Hilbert Space ◽  
Jacobson Radical ◽  
Compact Operators ◽  
General Algebra ◽  
Closed Algebra ◽  
Quasinilpotent Operators ◽  
Simultaneous Triangularization

AbstractIf A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.

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.

scholarly journals The Jacobson Radical for Analytic Crossed Products

2001 ◽  
Vol 187 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Allan P Donsig ◽  
Aristides Katavolos ◽  
Antonios Manoussos
Keyword(s):  
Jacobson Radical ◽  
Crossed Products
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