Add to ORKGAbstract. Let R ⊂ T be a minimal ring extension of (commutative inte-gral) domains. If R is integrally closed in T, then R is a going-down domain if and only if T is a going-down domain. The preceding assertion can be generalized to the context of weak Baer going-down rings. If R is integrally closed and T is a Prüfer domain, then R is a Prüfer domain. If T is integral over R and T is a going-down domain, then R is a going-down domain if and only if the extension R ⊂ T satisfies the going-down property. An example is given of an integral minimal overring extension R ⊂ T of two-dimensional domains such that T is a going-down (in fact, Prüfer) domain and R is a treed domain which is not a going-down domain. 1
LetRbe an integral domain. Forf∈R [ X ] letAfbe the ideal ofRgenerated by the coefficients off. We d...
Abstract. Given a pair of commutative rings R ( T with the same identity, T is a minimal ring extens...
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance,...
It is proved that if R is a 2-root closed two-dimensional going-down domain with no factor domain of...
It is proved that if R is a 2-root closed two-dimensional going-down domain with no factor domain of...
and T be integral domains with D _C T. The pair of domains D C _ T satisfies simple going down if D ...
Abstract. Let G be a group acting via ring automorphisms on a commu-tative unital ring R. If G is fi...
Abstract. A (commutative integral) domain R is called an AGU-domain if R ⊆ T satisfies the going-up ...
AbstractWe prove that a locally Jaffard integrally closed domain is such that each overring is treed...
AbstractWe prove that a locally Jaffard integrally closed domain is such that each overring is treed...
Abstract. Let R be a (commutative integral) domain and M a maximal ideal of R. Let T (M) be a minima...
Abstract. Let? be a semistar operation on a domain D. Then the semistar Nagata ring Na(D,?) is a tre...
Abstract. It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (fo...
AbstractAll rings considered are commutative with identity and all ring extensions are unital. Let R...
AbstractLet R be any integral domain. The minimal (commutative unital) ring extensions S of R are, u...
LetRbe an integral domain. Forf∈R [ X ] letAfbe the ideal ofRgenerated by the coefficients off. We d...
Abstract. Given a pair of commutative rings R ( T with the same identity, T is a minimal ring extens...
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance,...
It is proved that if R is a 2-root closed two-dimensional going-down domain with no factor domain of...
It is proved that if R is a 2-root closed two-dimensional going-down domain with no factor domain of...
and T be integral domains with D _C T. The pair of domains D C _ T satisfies simple going down if D ...
Abstract. Let G be a group acting via ring automorphisms on a commu-tative unital ring R. If G is fi...
Abstract. A (commutative integral) domain R is called an AGU-domain if R ⊆ T satisfies the going-up ...
AbstractWe prove that a locally Jaffard integrally closed domain is such that each overring is treed...
AbstractWe prove that a locally Jaffard integrally closed domain is such that each overring is treed...
Abstract. Let R be a (commutative integral) domain and M a maximal ideal of R. Let T (M) be a minima...
Abstract. Let? be a semistar operation on a domain D. Then the semistar Nagata ring Na(D,?) is a tre...
Abstract. It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (fo...
AbstractAll rings considered are commutative with identity and all ring extensions are unital. Let R...
AbstractLet R be any integral domain. The minimal (commutative unital) ring extensions S of R are, u...
LetRbe an integral domain. Forf∈R [ X ] letAfbe the ideal ofRgenerated by the coefficients off. We d...
Abstract. Given a pair of commutative rings R ( T with the same identity, T is a minimal ring extens...
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance,...