منابع مشابه
Projective Representations I. Projective lines over rings
We discuss representations of the projective line over a ring R with 1 in a projective space over some (not necessarily commutative) field K. Such a representation is based upon a (K,R)-bimodule U . The points of the projective line over R are represented by certain subspaces of the projective space P(K,U ×U) that are isomorphic to one of their complements. In particular, distant points go over...
متن کاملThe rings of noncommutative projective geometry
In the past 15 years a study of “noncommutative projective geometry” has flourished. By using and generalizing techniques of commutative projective geometry, one can study certain noncommutative graded rings and obtain results for which no purely algebraic proof is known. For instance, noncommutative graded domains of quadratic growth, or “noncommutative curves,” have now been classified by geo...
متن کاملMorphisms of projective spaces over rings
The fundamental theorem of projective geometry is generalized for projective spaces over rings. Let RM and SN be modules. Provided some weak conditions are satisfied, a morphism g : PðMÞnE ! PðNÞ between the associated projective spaces can be induced by a semilinear map f : M ! N. These conditions are satisfied for instance if S is a left Ore domain and if the image of g contains three indepen...
متن کاملProposition Algebra with Projective Limits
Sequential logic deviates from propositional logic by taking into account that atomic propositions yield different Boolean values at different times during the sequential evaluation of a single proposition. Reactive valuations capture this dynamics of a proposition’s environment. This logic is phrased as an equationally specified algebra rather than in the form of proof rules. It is strictly mo...
متن کاملCOTORSION DIMENSIONS OVER GROUP RINGS
Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1993
ISSN: 0022-4049
DOI: 10.1016/0022-4049(93)90017-n