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《代数通讯》2013,41(7):2827-2839
Abstract We study some one-sided ideals of row bounded and of column bounded matrix rings over free algebras. Obtained results are applied to answer several open problems on subhereditary radicals of associative rings. In particular we show that the right strongly prime radical is not left subhereditary and that the lattice of left (right) subhereditary radicals is not complete. 相似文献
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S. Tumurbat 《Acta Mathematica Hungarica》2001,93(1-2):99-108
Principally left strong radicals were introduced in [4]. Here, we continue to study such radicals. Principally left strong
radicals and their semisimple classes are characterized in Section 2. Sections 3 and 4 are devoted to the lower principally
left strong radical construction and to the upper principally left strong radical construction, respectively.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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A lattice-theoretic approach to the radical theory of rings was initiated by Snider. In the current paper, we extend this approach to the radical theory of involution rings. We show that the classes of hereditary radicals, radicals satisfying ADS and invariant radicals form complete sublattices of the lattice of all radicals of involution rings. We show that certain sublattices are isomorphic to sublattices of the lattice of radicals of rings. We characterize the atoms of certain lattices of radicals of involution rings.1991 Mathematics Subject Classification: 16W10, 16N99, 06B99 相似文献
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In this article we study the problem when a left distributive algebra over a field determines an atom of the lattice of all radicals of rings. We show that this problem is strictly connected with the problem of describing extensions of left chain algebras and give a characterization of left chain algebras determining atoms. 相似文献
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Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups
One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair. 相似文献
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We discuss several problems on the structure of nil rings from the linear algebra point of view. Among others, a number of questions and results are presented concerning algebras of infinite matrices over nil algebras, and nil algebras of infinite matrices over fields, which are related to the famous Koethe's problem. Some questions on radicals of tensor products of algebras related to Koethe's problem are also discussed. 相似文献
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Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal(right ideal,bi-ideal) is an ordered subsemigroup(resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal) by using some binary relations on S. 相似文献
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In this note we study the properties of Amitsur's example for Wedderburn radicals, introducing the concept of W n -reduced rings. The theories of commutative ring and reduced ring are generalized to W n -reduced rings. We characterize the W n -reduced property and study properties of W n -reduced rings. It is shown that the classes of semi-commutative rings, W n -reduced rings, and 2-primal rings are in a strictly increasing order. We extend the class of W n -reduced rings, observing various kinds of extensions containing classical quotient rings, polynomial rings, and power series rings. Communicated by M. Ferrero. 相似文献
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It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of topologicalradicals in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx. 相似文献
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设RP是环R上的左模.记P*= Hom R(P , R ) , J = P P*, S0= P*P.本文讨论了J与S的双零化理想格之间的关系,以及R,J,S0和EndRP的正规根之间的关系. 相似文献
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A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H). 相似文献
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We prove results relative to the problem of finding sharp bounds for the affine invariant . Namely, we prove that if K is a 3-dimensional zonoid of volume 1, then its second projection body is contained in 8K, while if K is any symmetric 3-dimensional convex body of volume 1, then contains 6K. Both inclusions are sharp. Consequences of these results include a stronger version of a reverse isoperimetric inequality for 3-dimensional zonoids established by the author in a previous work, a reduction for the 3-dimensional Petty conjecture to another isoperimetric problem and the best known lower bound up to date for in 3 dimensions. As byproduct of our methods, we establish an almost optimal lower bound for high-dimensional bodies of revolution. 相似文献
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In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1. 相似文献