Titlebook: Advances in Ring Theory; S. K. Jain,S. Tariq Rizvi Conference proceedings 1997 Springer Science+Business Media New York 1997 Excel.Finite.

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Decompositions of D1 Modules,l-extending (D1) modules, those modules which are supplemented and for which each supplement is a summand. The notions of hollowness and dual Goldie dimension play a prominent role. Our results are analogous to results for extending modules developed by Camillo and Yousif.

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On Extensions of Regular Rings of Finite Index by Central Elements,h is “almost biregular”, i.e., one where supports of elements in the Pierce sheaf are open. It is formed by adjoining certain central idempotents from .. Extensions of . by central elements, particularly idempotents, are examined. Many examples and counterexamples are presented.

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Weak Relative Injective ,-Subgenerated Modules,weakly .-injective in .[.]. Modules for which every submodule is weakly injective (tight) in .[.] are characterized. Modules . for which every module in .[.] is weakly injective and for which weakly injective modules are closed under direct sums are studied.

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Right Cones in Groups,he cones of (right) linearly ordered groups on the one hand and valuation rings, in particular right chain domains, on the other. The ideal theory of right cones is described, the rank one right cones are classified, and three problems are raised.

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Direct Product and Power Series Formations Over 2-Primal Rings,e sufficient conditions on the rings for their direct product to be 2-primal. We also show that the ring of formal power series over a 2-primal ring (or even a ring satisfying (PS I)) need not be 2-primal.