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Algebraic characterization of finite (branched) coverings

100%

Mulero M. A.

Fundamenta Mathematicae

1998

tom 158

nr 2

165-180

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism C(S) → C(X) is integral and flat.

Algebraic properties of rings of continuous functions

100%

Mulero M. A.

Fundamenta Mathematicae

1996

tom 149

nr 1

55-66

This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Mulero M. A.

1 1998

1 1996

Wyniki wyszukiwania

Algebraic characterization of finite (branched) coverings

Algebraic properties of rings of continuous functions