Abstract. A (commutative integral) domain R is called an AGU-domain if R ⊆ T satisfies the going-up property whenever T is an algebraic extension domain of R such that the natural map Spec(T) → Spec(R) sends the max-imal spectrum Max(T) onto Max(R). Any domain of (Krull) dimension 1 is an AGU-domain, as is any absolutely injective (ai-) domain. A quasilocal domain is an AGU-domain if and only if it is a going-down domain. A partial generalization is given for rings with nontrivial zero-divisors. An example is given of a two-dimensional Prüfer (hence going-down) domain with exactly two maximal ideals which is not an AGU-domain. 1
AbstractAn integral domain R is said to be an almost Bézout domain (respectively, almost GCD-domain)...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
The problem with which this investigation is concerned is that of determining the properties of the ...
Abstract. Let R ⊂ T be a minimal ring extension of (commutative inte-gral) domains. If R is integral...
Abstract. It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (fo...
Abstract. We introduce and develop the theory of “quasi-going-up do-mains, ” a concept dual to going...
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance,...
Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüf...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
Abstract. Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for...
and T be integral domains with D _C T. The pair of domains D C _ T satisfies simple going down if D ...
This work develops concepts related to the going-up property in commutative ring theory. In Chapter ...
Abstract. Let? be a semistar operation on a domain D. Then the semistar Nagata ring Na(D,?) is a tre...
AbstractThe rings of the title are the (not necessarily Noetherian) integral domains R such that R[X...
AbstractAn integral domain R is said to be an almost Bézout domain (respectively, almost GCD-domain)...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
The problem with which this investigation is concerned is that of determining the properties of the ...
Abstract. Let R ⊂ T be a minimal ring extension of (commutative inte-gral) domains. If R is integral...
Abstract. It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (fo...
Abstract. We introduce and develop the theory of “quasi-going-up do-mains, ” a concept dual to going...
It is proved that if R ⊂ T are going-down domains such that Spec(R) = Spec(T) as sets (for instance,...
Let D be an integral domain and X an indeterminate over D. It is well known that (a) D is quasi-Prüf...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
Abstract. Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for...
and T be integral domains with D _C T. The pair of domains D C _ T satisfies simple going down if D ...
This work develops concepts related to the going-up property in commutative ring theory. In Chapter ...
Abstract. Let? be a semistar operation on a domain D. Then the semistar Nagata ring Na(D,?) is a tre...
AbstractThe rings of the title are the (not necessarily Noetherian) integral domains R such that R[X...
AbstractAn integral domain R is said to be an almost Bézout domain (respectively, almost GCD-domain)...
summary:Let $R$ be a commutative ring with unity. The notion of maximal non valuation domain in an i...
The problem with which this investigation is concerned is that of determining the properties of the ...
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