Results 261 to 270 of about 3,828 (293)
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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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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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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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Topological Jacobson Radicals. III
Journal of Mathematical SciencesThe main results of the paper find sufficient conditions under which a radical (with or without some extra properties) is defined on some (subclass of a) class of (topological) algebras. The studied class is a variety of \(F\)-algebras in Section 2, a class of topological algebras over certain topological ring in Section 3 and a variety of topological ...
Glavatsky, S. T. +2 more
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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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Effective aspects of Jacobson radicals of rings
Mathematical Logic Quarterly, 2021AbstractThis paper studies effective aspects of Jacobson radicals of rings and their applications from the viewpoint of reverse mathematics. First, we propose four radicals of rings, showing that the first order (resp., second order) left and right Jacobson radical coincide in (resp., ).
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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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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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On the Jacobson radical of a semiring
Journal of Algebra and Its ApplicationsBased on the minimal and simple representations of semirings, we introduce two Jacobson-type Hoehnke radicals, namely, m-radical and s-radical, of a semiring [Formula: see text]. Every minimal (simple) [Formula: see text]-semimodule is a quotient of [Formula: see text] by a regular right congruence (maximal) [Formula: see text] on [Formula: see text ...
A. K. Bhuniya, Puja Sarkar
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