Results 61 to 70 of about 1,140 (171)
Modules in which semisimple fully invariant submodules are essential in summands
, 2019 One of the useful generalization of extending notion is FI-extending property. A module is called FI-extending if every fully invariant submodule is essential in a direct summand.
YAŞAR, RAMAZAN
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$k$ Summands of Syzygies over Rings of Positive Burch Index Via Canonical Resolutions
, 2023 In recent work, Dao and Eisenbud define the notion of a Burch index, expanding the notion of Burch rings of Dao, Kobayashi, and Takahashi, and show that for any module over a ring of Burch index at least 2, its $n$th syzygy contains direct summands of ...
Miller, Claudia, DeBellevue, Michael
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A Generic Characterization of Direct Summands for Orthogonal Involutions [PDF]
Communications in Algebra, 2009 The `transcendental methods' in the algebraic theory of quadratic forms are based on two major results, proved in the 60's by Cassels and Pfister, and known as the representation and the subform theorems. A generalization of the representation theorem was proven by Jean-Pierre Tignol in 1996, in the setting of central simple algebras with involution ...
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Decomposition of polynomial matrices into a direct sum of triangular summands
, 1999 Многочлениа матриця A(x), елементарні дільники якої попарно взаємно прості, перетвореннями SA(x)R(x), де S,R(х) -оборотні матриці, зводиться до прямої суми незвідних трикутних доданків з інваріантними множниками на головних діагоналях.By using the ...
Шаваровський, Б.З.
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, 1984 We prove the direct sum conjecture for various sets of systems of bilinear forms. Our results depend on a priori knowledge of the complexity of at least one of the direct summands and its underlying algebraic structure.
Winograd, Shmuel, Feig, Ephraim
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Direct Summand of Serial Modules
European Journal of Pure and Applied MathematicsLet R be an associative ring and M a unitary left R-module. An R-module M is said to be uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum of uniserial modules. In this paper, we bring our modest contribution to the open problem listed in the book of Alberto Facchini "Module Theory" which states that is any ...
Alhousseynou BA +2 more
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Direct sums of bilinear algorithms
, 1981 We consider the bilinear complexity of certain sets of bilinear forms. We study a class of direct sums of bilinear forms. For this class of problems we show that the bilinear complexity of one direct sum is the sum of the bilinear complexities of the ...
Winograd, S., Auslander, L., Feig, E.
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Cancellation and direct summands in dimension 1
, 1991 Let Λ be a module-finite algebra over a commutative noetherian ring of Krull dimension 1. We extend Roiter's direct-summand theorem to arbitrary finitely generated Λ-modules, obtaining a sharpened form of Serre's direct-summand theorem in this setting ...
Levy, Lawrence S, Guralnick, Robert M
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On modules that complement direct summands
Osaka Journal of Mathematics, 1986 An R-module M is said to ''complement direct summands'' if for every direct summand B of M and for every decomposition \(M=\oplus_{i\in I}A_ i\), where every \(A_ i\) is completely incomposable, there exists a subset K of the index set I with \(M=B\oplus (\oplus_{k\in K}A_ k)\). The following characterizations are mentioned by \textit{M. Harada} [Publ.
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Multiplicative complexity of direct sums of quadratic systems
, 1995 We consider the quadratic complexity of certain sets of quadratic forms. We study 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 complexities of the summands and ...
Nader H. Bshouty, Bshouty, Nader H.
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