Displaying similar documents to “On isomorphisms between σ -ideals on ω 1 ”

Structural properties of ideals

J. E. Baumgartner, A. D. Taylor, S. Wagon

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CONTENTSPreface.............................................................................................. 5Chapter I. Preliminaries................................................................. 61. Notation and terminology.......................................................... 62. Results from the literature......................................................... 93. Definitions and basic properties.............................................. 11Chapter II. Subnormality and...

Rothberger gaps in fragmented ideals

Jörg Brendle, Diego Alejandro Mejía (2014)

Fundamenta Mathematicae

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The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of F σ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...

Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra

Deng Yin Wang, Haishan Pan, Xuansheng Wang (2010)

Czechoslovak Mathematical Journal

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Let 𝒫 be an arbitrary parabolic subalgebra of a simple associative F -algebra. The ideals of 𝒫 are determined completely; Each ideal of 𝒫 is shown to be generated by one element; Every non-linear invertible map on 𝒫 that preserves ideals is described in an explicit formula.