Displaying similar documents to “Sum and difference free partitions of vector spaces”

Vector sets with no repeated differences

Péter Komjáth (1993)

Colloquium Mathematicae

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We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is “yes” if the set is of size at most ℵ 2 , “not” if the set is allowed to be of size ( 2 2 ℵ 0 ) + . It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.

Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that E x t R ( G , G ) = 0 . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...

L ∞ -Khintchine-Bonami inequality in free probability

Artur Buchholz (1998)

Banach Center Publications

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We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ( f = ∑ | w | = l a w ⊗ λ ( w ) ). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

Large free set

Kandasamy Muthuvel (1992)

Colloquium Mathematicae

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