Displaying similar documents to “ Spec ( R ) and separation axioms between T 0 and T 1 .”

On Strong Going-Between, Going-Down, And Their Universalizations, II

David E. Dobbs, Gabriel Picavet (2003)

Annales mathématiques Blaise Pascal

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We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if A ⊆ B are domains such that A is an LFD universally going-down domain and B is algebraic over A , then the inclusion map A [ X 1 , ⋯ , X n ] ↪ B [ X 1 , ⋯ , X n ] satisfies GB for each n ≥ 0 . However, for any...

On the maximal spectrum of commutative semiprimitive rings

K. Samei (2000)

Colloquium Mathematicae

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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).