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The direct sum of universal relations
Information Processing Letters, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on direct sums of Friedbergnumberings
Journal of Symbolic Logic, 1989We show that a translator ƒ: ω → ω from a Gödelnumbering φ into a direct sum η of a r.e. family of Friedbergnumberings satisfies ƒ ≰T0′. In particular, η cannot be a Gödelnumbering.In the following we use standard notation (cf.[3]): for i ≥ 1, Pi (respectively, Ri) is the set of partial (total) recursive i-place functions; φ is a Gödel numbering of P1.
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On a direct sum of irreducible groups
Mathematical Notes, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Boletín de la Sociedad Matemática Mexicana, 2015
Let \(R\) be an associative ring with an identity element. A unital right \(R\)-module \(M\) is called ADS* if for any direct summand \(N\) of \(M\) and any supplement \(K\) of \(N\) in \(M\) one has \(M=N\oplus K\). The aim of this paper is to investigate direct sums of ADS* modules. First, the authors provide a bunch of examples of ADS* modules whose
Tribak, Rachid +2 more
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Let \(R\) be an associative ring with an identity element. A unital right \(R\)-module \(M\) is called ADS* if for any direct summand \(N\) of \(M\) and any supplement \(K\) of \(N\) in \(M\) one has \(M=N\oplus K\). The aim of this paper is to investigate direct sums of ADS* modules. First, the authors provide a bunch of examples of ADS* modules whose
Tribak, Rachid +2 more
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Advances in Operator Theory, 2023
Let \(A\) be a square matrix partitioned as follows: \[ A = \left[ \begin{array}{cc} B & C \\ D & E \end{array} \right]. \] The authors study several sufficient conditions on \(A\) to assure that \(A\) is a direct sum of \(B\) and \(C\), i.e., \(C=0\) and \(D=0\).
Hwa-Long Gau, Pei Yuan Wu
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Let \(A\) be a square matrix partitioned as follows: \[ A = \left[ \begin{array}{cc} B & C \\ D & E \end{array} \right]. \] The authors study several sufficient conditions on \(A\) to assure that \(A\) is a direct sum of \(B\) and \(C\), i.e., \(C=0\) and \(D=0\).
Hwa-Long Gau, Pei Yuan Wu
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Communications in Algebra, 1974
It is a well-known result that the direct sum of any family of injective modules over a Noetherian ring is injective. Conversely, if A is a ring with the property that the direct sum of any family of injective modules is injective H. Bass [1] has shown that A is Noetherian.
B. Sarath, K. Varadarajan
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It is a well-known result that the direct sum of any family of injective modules over a Noetherian ring is injective. Conversely, if A is a ring with the property that the direct sum of any family of injective modules is injective H. Bass [1] has shown that A is Noetherian.
B. Sarath, K. Varadarajan
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Direct Sums and Direct Products
2015The concept of direct sum is of utmost importance for the theory. This is mostly due to two facts: first, if we succeed in decomposing a group into a direct sum, then it can be studied by investigating the summands separately, which are, in numerous cases, simpler to deal with.
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DIRECT SUMS OF OPERATOR SPACES
Journal of the London Mathematical Society, 2001It is proved that if X and Y are operator spaces such that every completely bounded operator from X into Y is completely compact and Z is a completely complemented subspace of X [oplus ] Y, then there exists a completely bounded automorphism τ: X [oplus ] Y → X [oplus ] Y with completely bounded inverse such that τZ = X0 [oplus ] Y0, where ...
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On the extended direct sum conjecture
Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89, 1989We consider the quadratic complexity of certain sets of quadratic forms. We study a classes of direct sums of quadratic forms. For these classes of problems we show that the complexity of one direct sum is the sum of the complexity of the summands and that every minimal quadratic algorithm for computing the direct sums is a direct-sum algorithm.
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2002
In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V, a direct sum decomposition of the form V = W ⊕W⊥. We now consider the following general notion.
T. S. Blyth, E. F. Robertson
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In Theorem 2.6 we obtained, for an inner product space V and a finite-dimensional subspace W of V, a direct sum decomposition of the form V = W ⊕W⊥. We now consider the following general notion.
T. S. Blyth, E. F. Robertson
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