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A primrose path from Krull to Zorn

Marcel Erné (1995)

Commentationes Mathematicae Universitatis Carolinae

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 $S \mapsto R S$ 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 $S \subseteq P (X)$ of finite character are in one-to-one correspondence with the conservative prime ideals contained in $P_{S} = ⋃ {R S : S \in S}$ , and the maximal members of $S$ correspond to the maximal ideals contained in...

A subspace of $S p e c (A)$ and its connexions with the maximal ring of quotients

Giuliano Artico, Umberto Marconi, Roberto Moresco (1981)

Rendiconti del Seminario Matematico della Università di Padova

Algébricité des fonctions méromorphes prenant certaines valeurs algébriques

Gérard Rauzy (1968)

Bulletin de la Société Mathématique de France

An application of modules of generalized fractions to grades of ideals and Gorenstein rings

H. Zakeri (1994)

Colloquium Mathematicae

Anneaux de Goldman

Jean Guérindon (1969/1970)

Séminaire Dubreil. Algèbre et théorie des nombres

Avoidance principle and intersection property for a class of rings

Rahul Kumar, Atul Gaur (2020)

Czechoslovak Mathematical Journal

Let $R$ be a commutative ring with identity. If a ring $R$ is contained in an arbitrary union of rings, then $R$ is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in $R$ , then $R$ contains one of them under various conditions.