Displaying similar documents to “On $a$-Kasch spaces”

Irreducibility of ideals in a one-dimensional analytically irreducible ring

Valentina Barucci, Faten Khouja (2010)

Actes des rencontres du CIRM

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Let R be a one-dimensional analytically irreducible ring and let I be an integral ideal of R . We study the relation between the irreducibility of the ideal I in R and the irreducibility of the corresponding semigroup ideal v ( I ) . It turns out that if v ( I ) is irreducible, then I is irreducible, but the converse does not hold in general. We collect some known results taken from [], [], [] to obtain this result, which is new. We finally give an algorithm to compute the components of an irredundant...

On almost discrete space

Ali Akbar Estaji (2008)

Archivum Mathematicum

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Let C ( X ) be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of C ( X ) . The intersection of essential weak ideal in C ( X ) is also studied.

On spaces with the ideal convergence property

Jakub Jasinski, Ireneusz Recław (2008)

Colloquium Mathematicae

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Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to I b , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.