Projective Groups over Rings
نویسندگان
چکیده
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...
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This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...
متن کاملOn Projective Geometry over Full Matrix Rings
1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...
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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...
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Serre [5] has recently proved a general theorem about projective modules over commutative rings. This theorem has the following consequence : If 7T is a finite abelian group, any finitely generated projective module over the integral group ring Zir is the direct sum of a free module and an ideal of Zir. The question naturally arises as to whether this result holds for nonabelian groups x. Serre...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9064