Results 1 to 10 of about 3,406,500 (137)

Direct sum decompositions and indecomposable TQFTs [PDF]

Journal of Mathematical Physics, 1995
The decomposition of an arbitrary axiomatic topological quantum field theory or TQFT into indecomposable theories is given. In particular, unitary TQFTs in arbitrary dimensions are shown to decompose into a sum of theories in which the Hilbert space of the sphere is one-dimensional, and indecomposable two-dimensional theories are classified.
Sawin, Stephen
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Partially Coherent Direct Sum Channels [PDF]

Quantum, 2021
We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are degradable, and provide a simplified expression for their quantum capacities.
Stefano Chessa, Vittorio Giovannetti
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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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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, Rizvi, S. Tariq, Roman, Cosmin S.   +2 more
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Computing direct sum decompositions

Journal of Symbolic Computation
We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the computation of indecomposable summands of coherent sheaves on subvarieties of toric varieties (in particular, for ...
Devlin Mallory, Mahrud Sayrafi
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Powers and direct sums

Journal of Mathematical Analysis and Applications, 2014
Abstract This paper investigates when a bounded operator on Hilbert space has the property that its square is similar to to the direct sum of it with itself. A few general results are obtained and the normal operators and unilateral shifts having this property are characterized. Several additional examples are explored.
John B. Conway, Gabriel Prǎjiturǎ, Alejandro Rodríguez-Martínez   +2 more
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Direct sums of ideals

Linear Algebra and its Applications, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heitmann, Raymond, Wiegand, Roger
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The direct sum of q-matroids

Journal of Algebraic Combinatorics
AbstractFor classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for q-matroids, the q-analogue of matroids. This is a lot less straightforward than in the classical case, as we will try to convince the reader.
Michela Ceria, Relinde Jurrius
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Cancellation in direct sums of groups [PDF]

Proceedings of the American Mathematical Society, 1956
5. L. K. Hua, A note on the total matrix ring over a non-commutative field, Annales de la Soci&t6 Polonaise de Math6matique vol. 25 (1952) pp. 188-198. 6. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 479-502. 7. F. Kasch, Invariante Untermoduln des Endomorphismenrings eines Vektorraums, Archiv
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