Displaying similar documents to “Conditions under which R ( x ) and R 〈 x 〉 are almost Q-rings”

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

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A lattice-ordered ring ℝ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f -rings ℝ such that ℝ / 𝕀 is contained in an f -ring with an identity element that is a strong order unit for some nil l -ideal 𝕀 of ℝ . In particular, if P ( ℝ ) denotes the set of nilpotent elements of the f -ring ℝ , then ℝ is an OIRI-ring if and only if ℝ / P ( ℝ ) is contained in an f -ring with an identity element that is a strong order unit. ...

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

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Let R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime. Let now σ be an automorphism of R and δ a σ -derivation of R . Then R is said to be an almost δ -divided ring if every minimal prime ideal of R is δ -divided. Let R be a Noetherian ring which is also an algebra over ℚ ( ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ ( * ) -ring and δ a σ -derivation of R such that σ ( δ ( a ) ) = δ ( σ ( a ) ) for all a ∈ R . Further,...

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...

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...