The Jacobson Radical for Analytic Crossed Products

Let J(R) be the Jacobson radical of a ring R. Then R is called homogeneous semilocal if R/J(R) is simple artinian. The aim of this paper is to find necessary and sufficient conditions for the group rings and the crossed products to be homogeneous semilocal ring.

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Locating the radical of a triangular operator algebra

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100071899 ◽

1994 ◽

Vol 115 (1) ◽

pp. 27-38 ◽

Cited By ~ 4

Author(s):

Laura Mastrangelo ◽

Paul S. Muhly ◽

Baruch Solel

Keyword(s):

Operator Algebra ◽

Jacobson Radical ◽

Sufficient Conditions ◽

Primary Objective ◽

Necessary And Sufficient Conditions ◽

Explicit Description ◽

Crossed Products ◽

Triangular Operator ◽

Necessary And Sufficient

AbstractOur primary objective is to give necessary and sufficient conditions for a triangular subalgebra of a groupoid C-algebra to be semisimple, i.e. to have vanishing Jacobson radical. If, in addition, the subalgebra is the analytic subalgebra determined by a real-valued cocycle on the groupoid, then we can give an explicit description of the radical in terms of the cocycle. As a consequence of this analysis, we are able to determine when certain analytic crossed products are semisimple.

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Homological dimensions of smooth crossed products

Annals of Functional Analysis ◽

10.1007/s43034-021-00125-w ◽

2021 ◽

Vol 12 (3) ◽

Author(s):

Petr Kosenko

Keyword(s):

Crossed Products ◽

Homological Dimensions

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

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2008/741609 ◽

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.

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Simultaneous Triangularization of Algebras of Polynomially Compact Operators

Canadian Mathematical Bulletin ◽

10.4153/cmb-1991-042-6 ◽

1991 ◽

Vol 34 (2) ◽

pp. 260-264 ◽

Cited By ~ 1

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.

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