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Displaying similar documents to “Atomicity and the fixed divisor in certain pullback constructions”

Boundary map and overrings of half-factorial domains

Nathalie Gonzalez, Sébastien Pellerin (2005)

Bollettino dell'Unione Matematica Italiana

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We investigate factorization of elements in overrings of a half-factorial domain A in relation with the behaviour of the boundary map of A . It turns out that a condition, called C ⋆ , on the extension plays a central role in this study. We finally apply our results to the special case of A + X ⁢ B ⁢ X polynomial rings.

Elasticity of A + XB[X] when A ⊂ B is a minimal extension of integral domains

Ahmed Ayache, Hanen Monceur (2011)

Colloquium Mathematicae

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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.

On Hardy spaces on worm domains

Alessandro Monguzzi (2016)

Concrete Operators

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In this review article we present the problem of studying Hardy spaces and the related Szeg˝o projection on worm domains. We review the importance of the Diederich–Fornæss worm domain as a smooth bounded pseudoconvex domain whose Bergman projection does not preserve Sobolev spaces of sufficiently high order and we highlight which difficulties arise in studying the same problem for the Szeg˝o projection. Finally, we announce and discuss the results we have obtained so far in the setting...