On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
Umberto Zannier (1995)
Acta Arithmetica
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Umberto Zannier (1995)
Acta Arithmetica
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J. R. Merriman, S. Siksek, N. P. Smart (1996)
Acta Arithmetica
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D. Benson, G. Gnacadja (1999)
Fundamenta Mathematicae
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Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms...
Ludomir Newelski (1996)
Fundamenta Mathematicae
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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
James Cummings, Mirna Džamonja, Saharon Shelah (1995)
Fundamenta Mathematicae
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D. Benson, Jon Carlson, Jeremy Rickard (1997)
Fundamenta Mathematicae
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We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories...
Ilijas Farah (1996)
Fundamenta Mathematicae
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We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).