Ore extensions over near pseudo-valuation rings.

Bhat, V.K.

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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).

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Wilson’s theorem

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We show how K. Hensel could have extended Wilson’s theorem from $Z$ to the ring of integers $𝔬$ in a number field, to find the product of all invertible elements of a finite quotient of $𝔬$ .