Displaying similar documents to “Isolated points and redundancy”

Pseudo-valuation rings. II

David F. Anderson, Ayman Badawi, David E. Dobbs (2000)

Bollettino dell'Unione Matematica Italiana

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Viene data una condizione sufficiente affinchè un sopra-anello di un anello di pseudo-valutazione (PVR) sia ancora un PVR. Da ciò segue che se R , M è un PVR, allora ogni sopra-anello di R è un PVR se (e soltanto se) R u è quasi-locale per ciascun elemento u di M : M . Vari risultati sono dimostrati per un ideale primo di un anello commutativo arbitrario R , avente Z R come insieme di zero-divisori. Per esempio, se P è un primo «forte» di R e contiene un elemento non-zero divisore di R , allora P : P è...

A primrose path from Krull to Zorn

Marcel Erné (1995)

Commentationes Mathematicae Universitatis Carolinae

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Given a set X of “indeterminates” and a field F , an ideal in the polynomial ring R = F [ X ] is called conservative if it contains with any polynomial all of its monomials. The map S R S yields an isomorphism between the power set P ( X ) and the complete lattice of all conservative prime ideals of R . Moreover, the members of any system S P ( X ) of finite character are in one-to-one correspondence with the conservative prime ideals contained in P S = { R S : S S } , and the maximal members of S correspond to the maximal ideals contained...

Rings of continuous functions vanishing at infinity

Ali Rezaei Aliabad, F. Azarpanah, M. Namdari (2004)

Commentationes Mathematicae Universitatis Carolinae

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We prove that a Hausdorff space X is locally compact if and only if its topology coincides with the weak topology induced by C ( X ) . It is shown that for a Hausdorff space X , there exists a locally compact Hausdorff space Y such that C ( X ) C ( Y ) . It is also shown that for locally compact spaces X and Y , C ( X ) C ( Y ) if and only if X Y . Prime ideals in C ( X ) are uniquely represented by a class of prime ideals in C * ( X ) . -compact spaces are introduced and it turns out that a locally compact space X is -compact if and only...