Results 141 to 150 of about 62,478 (178)
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HOPF-JACOBSON RADICAL FOR COMODULE ALGEBRAS
Chinese Annals of Mathematics, 1999Let \(H\) be a Hopf algebra, and \(A\) a right \(H\)-comodule algebra (not necessarily with identity). The relation between the Hopf-Jacobson radical \(J^H(A)\) and the Jacobson radical of the smash product \(J(A\#H^{*\text{rat}}\)) is studied. A version of the density theorem for simple left relative Hopf modules is given.
Cai, Chuanren, Guo, Guangquan
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The topological jacobson radical of rings. II
Journal of Mathematical Sciences, 2012The authors continue their study of the topological Jacobson radical of topological rings started in part I [J. Math. Sci., New York 185, No. 2, 207-220 (2012); translation from Fundam. Prikl. Mat. 16, No. 8, 49-68 (2010; Zbl 1262.16049)]. They show that a primitive topological ring possesses a faithful topologically irreducible module. They also prove
Glavatsky, S. T. +2 more
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1993
In Chapter One we developed a structure theory for semisimple rings, as summarized in Theorem 1.18. This theory used, for the most part, properties of modules over a semisimple ring in order to characterize such a ring. In this chapter, we give a more intrinsic characterization of semisimple rings.
Benson Farb, R. Keith Dennis
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In Chapter One we developed a structure theory for semisimple rings, as summarized in Theorem 1.18. This theory used, for the most part, properties of modules over a semisimple ring in order to characterize such a ring. In this chapter, we give a more intrinsic characterization of semisimple rings.
Benson Farb, R. Keith Dennis
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1994
This chapter has as its major goal the creation of the first steps needed to construct a general structure theory for associative rings. The aim of any structure theory is the description of some general objects in terms of some simpler ones—simpler in some perceptible sense, perhaps in terms of concreteness, perhaps in terms of tractability.
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This chapter has as its major goal the creation of the first steps needed to construct a general structure theory for associative rings. The aim of any structure theory is the description of some general objects in terms of some simpler ones—simpler in some perceptible sense, perhaps in terms of concreteness, perhaps in terms of tractability.
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ON THE JACOBSON RADICAL OF GRADED RINGS
Communications in Algebra, 2001Let S be a semigroup. A ring R is said to be S-graded if R = s ∈ S R s is a direct sum of additive subgroups R s and R s R t ⊆ R st for all s, t ∈ S.
Jespers, Eric +2 more
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The Jacobson Radical and Regular Modules
Canadian Mathematical Bulletin, 1975Let A be an associative, but not necessarily commutative, ring with identity, and J = J(A) its Jacobson radical. A (unital) module is regular iff every submodule is pure (see (1)). The regular socle R(M) of a module M is the sum of all its submodules which are regular. These concepts have been introduced and studied in (2).
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1991
Historically, the notion of the radical was a direct outgrowth of the notion of semisimplicity. It may be somewhat surprising, however, to remark that the radical was studied first in the context of nonassociative rings (namely, finite-dimensional Lie algebras) rather than associative rings. In the work of E. Cartan, the radical of a finite-dimensional
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Historically, the notion of the radical was a direct outgrowth of the notion of semisimplicity. It may be somewhat surprising, however, to remark that the radical was studied first in the context of nonassociative rings (namely, finite-dimensional Lie algebras) rather than associative rings. In the work of E. Cartan, the radical of a finite-dimensional
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On Jacobson Near-rings and Special Radicals
Algebra Colloquium, 2007In this paper, we construct special radicals using class pairs of near-rings. We establish necessary conditions for a class pair to be a special radical class. We then define Jacobson-type near-rings and show that in most cases the class of all near-rings of this type is a special radical class.
Godloza, L. +2 more
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On partial H-radicals of Jacobson type
São Paulo Journal of Mathematical Sciences, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rafael Cavalheiro, Alveri Sant’Ana
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Noetherian rings with projective jacobson radical
Communications in Algebra, 1985(1985). Noetherian rings with projective jacobson radical. Communications in Algebra: Vol. 13, No. 6, pp. 1359-1366.
A.W. Chatters, C.R. Hajarnavis
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