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Displaying similar documents to “Normalizing extensions of semiprime rings.”

Prime ideals in semirings.

Gupta, Vishnu, Chaudhari, J.N. (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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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).

A “class group” obstruction for the equation C y d = F ( x , z )

Denis Simon (2008)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we study equations of the form C y d = F ( x , z ) , where F ∈ ℤ [ x , z ] is a binary form, homogeneous of degree n , which is supposed to be primitive and irreducible, and d is any fixed integer. Using classical tools in algebraic number theory, we prove that the existence of a proper solution for this equation implies the existence of an integral ideal of given norm in some order in a number field, and also the existence of a specific relation in the class group involving this ideal. In some cases,...