On the computation of minimal reduction.

Bod'a, E.; Šuňal, I.

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Ali, Majid M. (2006)

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Integral closures of ideals in the Rees ring

Y. Tiraş (1993)

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The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.

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On the maximal spectrum of commutative semiprimitive rings

K. Samei (2000)

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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).