Results 11 to 20 of about 600,006 (325)
Direct sums of Rickart modules
Journal of Algebra, 2012 A right \(R\)-module \(M\) with endomorphism ring \(S=\text{End}_R(M)\) is called a Rickart module if the right annihilator in \(M\) of any single element of \(S\) is a direct summand of \(M\). In general, the class of Rickart modules is not closed under direct sums, and it is interesting to study when it has this closure property.
Lee, Gangyong +2 more
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Algebraic entropies, Hopficity and co-Hopficity of direct sums of Abelian Groups
Topological Algebra and its Applications, 2015 Necessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups.We ...
Goldsmith Brendan, Gong Ketao
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Extended Weyl-Type Theorems for Direct Sums
Demonstratio Mathematica, 2014 In this paper, we study the stability of extended Weyl and Browdertype theorems for orthogonal direct sum S⊕T, where S and T are bounded linear operators acting on Banach space.
Berkani M., Kachad M., Zariouh H.
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Direct sums and the Szlenk index [PDF]
Journal of Functional Analysis, 2011 Philip A. H. Brooker
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On direct sums of Baer modules
Journal of Algebra, 2009 A ring \(R\) is called Baer if the left annihilator of every nonempty subset of \(R\) is generated by an idempotent. In a general module theoretic setting, the concept of a Baer module was defined by the present authors [in Commun. Algebra 32, No. 1, 103-123 (2004; Zbl 1072.16007)] in terms of its endomorphism ring. Indeed, a right \(R\)-module \(M_R\)
Rizvi, S. Tariq, Roman, Cosmin S.
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Distributive lattices with strong endomorphism kernel property as direct sums [PDF]
Categories and General Algebraic Structures with Applications, 2020 Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (
Jaroslav Gurican
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A-Browder-type theorems for direct sums of operators [PDF]
Mathematica Bohemica, 2016 We study the stability of a-Browder-type theorems for orthogonal direct sums of operators. We give counterexamples which show that in general the properties $(\rm SBaw)$, $(\rm SBab)$, $(\rm SBw)$ and $(\rm SBb)$ are not preserved under direct sums of ...
Mohammed Berkani +2 more
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On reflexivity of direct sums [PDF]
Proceedings of the American Mathematical Society, 2000 Summary: Necessary and sufficient conditions are presented to insure that the direct sum of two reflexive representations of a finite-dimensional algebra is reflexive, and it is shown that for each such algebra, there is an integer \(k\) such that the direct sum of \(k\) copies of each of its representations is reflexive.
Camillo, V. P., Fuller, K. R.
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DIRECT SUMS OF INFINITELY MANY KERNELS [PDF]
Journal of the Australian Mathematical Society, 2010 AbstractLet 𝒦 be the class of all rightR-modules that are kernels of nonzero homomorphisms φ:E1→E2for some pair of indecomposable injective rightR-modulesE1,E2. In a previous paper, we completely characterized when two direct sumsA1⊕⋯⊕AnandB1⊕⋯⊕Bmof finitely many modulesAiand Bjin 𝒦 are isomorphic.
ECEVIT S, FACCHINI, ALBERTO, KOSAN M. T.
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Proximinality in generalized direct sums
International Journal of Mathematics and Mathematical Sciences, 2004 We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.
Darapaneni Narayana, T. S. S. R. K. Rao
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