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ℵ k -free separable groups with prescribed endomorphism ring

Daniel Herden, Héctor Gabriel Salazar Pedroza (2015)

Fundamenta Mathematicae

We will consider unital rings A with free additive group, and want to construct (in ZFC) for each natural number k a family of ℵ k -free A-modules G which are separable as abelian groups with special decompositions. Recall that an A-module G is ℵ k -free if every subset of size < ℵ k is contained in a free submodule (we will refine this in Definition 3.2); and it is separable as an abelian group if any finite subset of G is contained in a free direct summand of G. Despite the fact that such a module G is...

2-local Lie isomorphisms of operator algebras on Banach spaces

Lin Chen, Lizhong Huang, Fangyan Lu (2015)

Studia Mathematica

Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.

[unknown]

Alessandro Ardizzoni, Federica Galluzzi, Francesco Vaccarino (0)

Annales de l’institut Fourier

Λ-modules and holomorphic Lie algebroid connections

Pietro Tortella (2012)

Open Mathematics

Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and ≡ : G r Λ → S y m • 𝒪 X 𝒢 is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on 𝒢 and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable...

τ -supplemented modules and τ -weakly supplemented modules

Muhammet Tamer Koşan (2007)

Archivum Mathematicum

Given a hereditary torsion theory τ = ( 𝕋 , 𝔽 ) in Mod- R , a module M is called τ -supplemented if every submodule A of M contains a direct summand C of M with A / C τ - torsion. A submodule V of M is called τ -supplement of U in M if U + V = M and U ∩ V ≤ τ ( V ) and M is τ -weakly supplemented if every submodule...

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