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Projectivities over local rings

✍ Scribed by Nirmala B. Limaye


Publisher
Springer-Verlag
Year
1971
Tongue
French
Weight
304 KB
Volume
121
Category
Article
ISSN
0025-5874

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We show that the following two conditions, for each integer r G 1, are equivalent for a finitely generated module M over a complete Noetherian local ring Ε½ . R, α’Š : embeddable in E r , where E denotes the injective hull of the residue field Rrα’Š. Ε½ . r Ε½ . b Either M ; E , or else dim Hom Rrα’Š, M s k

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In this paper, MÀurer's theorems characterizing certain subgroups of the projective group PGL 2 K over a field K are generalized to the case of rings.  2002 Elsevier Science (USA)

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## Abstract We show that the bicategory whose 0‐cells are corings over rings with local units is bi‐equivalent to the bicategory of comonads in (right) unital modules whose underlying functors are right exact and preserve direct sums. A base ring extension of a coring by an adjunction is introduced

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Let R, m be a local ring commutative and Noetherian . If R is complete or, . more generally, Henselian , one has the Krull᎐Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion R, we can get a measure of how badly the Krull᎐Sch