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Construction of p o -groups with quasi-divisors theory

Jiří Močkoř (2000)

Czechoslovak Mathematical Journal

A method is presented making it possible to construct p o -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups H ( Δ , ) , where Δ are finitely atomic root systems. Some examples of these constructions are presented.

Large superdecomposable E(R)-algebras

Laszlo Fuchs, Rüdiger Göbel (2005)

Fundamenta Mathematicae

For many domains R (including all Dedekind domains of characteristic 0 that are not fields or complete discrete valuation domains) we construct arbitrarily large superdecomposable R-algebras A that are at the same time E(R)-algebras. Here "superdecomposable" means that A admits no (directly) indecomposable R-algebra summands ≠ 0 and "E(R)-algebra" refers to the property that every R-endomorphism of the R-module, A is multiplication by an element of, A.

Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces

Othman Echi (2003)

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of quasi-homeomorphisms, the Goldman prime spectrum and the Jacobson prime spectrum of a commutative ring. We prove that, if g : Y X is a quasi-homeomorphism, Z a sober space and f : Y Z a continuous map, then there exists a unique continuous map F : X Z such that F g = f . Let X be a T 0 -space, q : X s X the injection of X onto its sobrification X s . It is shown, here, that q Gold X = Gold X s , where Gold X is the set of all locally closed points of X . Some applications are also indicated. The Jacobson prime spectrum...

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