Results 91 to 100 of about 1,167 (194)
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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Kitaoka's conjecture and sums of squares
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract We connect the existence of a ternary classical universal quadratic form over a totally real number field K$K$ with the property that all totally positive multiples of 2 are sums of squares (if K$K$ does not contain 2$\sqrt{2}$ or contains a nonsquare totally positive unit).
Vítězslav Kala +2 more
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MODULES WHOSE CLOSED SUBMODULES WITH ESSENTIAL SOCLE ARE DIRECT SUMMANDS [PDF]
, 2014 We introduce and study CLESS-modules, which subsume two generalizations of extending modules due to P.F. Smith and A. Tercan. A module M will be called a CLESS-module if every closed submodule N of M (in the sense that M/N is non-singular) with essential
Sahinkaya, Serap, Crivei, Septimiu
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The number of regular simplices in higher dimensions
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract We study the extremal function Sdk(n)$S^k_d(n)$, defined as the maximum number of regular (k−1)$(k-1)$‐simplices spanned by n$n$ points in Rd$\mathbb {R}^d$. For any fixed d⩾2k⩾6$d\geqslant 2k\geqslant 6$, we determine the asymptotic behavior of Sdk(n)$S^k_d(n)$ up to a lower‐order term.
Felix Christian Clemen +2 more
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On rings whose left modules are direct sums of finitely generated modules [PDF]
, 1976 The relationship between rings of finite module type and rings whose left modules have decompositions that complement direct summands is examined by proving that the latter are precisely the rings of the title.
Kent R. Fuller
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When is the graph of a random 0/1 polytope a clique?
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract We study graph‐theoretic properties of random 0/1$0/1$ polytopes. Specifically, let Qpn⊆{0,1}n$Q_p^n \subseteq \lbrace 0,1\rbrace ^n$ be a random subset where each point is included independently with probability p$p$, and consider the graph Gp$G_p$ of the polytope conv(Qpn)$\operatorname{conv}(Q_p^n)$.
Catherine Babecki +2 more
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A birational description of the minimal exponent
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.
Qianyu Chen, Mircea Mustaţă
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Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract In 1973, Erdős conjectured the existence of high girth (n,3,2)$(n,3,2)$‐Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Recently, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture.
Michelle Delcourt, Luke Postle
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High Relative Accuracy Computations With Covariance Matrices of Order Statistics
Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 11794-11810, 30 July 2026.ABSTRACT In many statistical applications, numerical computations with covariance matrices need to be performed. The error made when performing such numerical computations increases with the condition number of the covariance matrix, which is related to the number of variables and the strength of the correlation between the variables. In a recent work,
Juan Baz +3 more
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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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