Invariant sets of morphisms on projective and affine number spaces
نویسندگان
چکیده
منابع مشابه
Affine Spaces within Projective Spaces
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finitedimensional or pappian. Mathematics Subject Classification...
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 کاملOn Discrete Borel Spaces and Projective Sets
Let J denote the unit interval, S—IXI the unit square; Cj and Cs the class of all subsets of I and 6, respectively. By Cj X Cj is meant the or-algebra on S generated by rectangles with sides in C/. The purpose of this note is to prove the following theorem (which settles a problem of S. M. Ulam) and observe some of its consequences. Without explicit mention, the axiom of choice has been assumed...
متن کاملCharacterizations of Finite Projective and Affine Spaces
THEOREM 1. A finite incidence structure is isomorphic to the design of points and hyperplanes of a finite projective or affine space of dimension greater than or equal to 4 if and only if there are positive integers v, k, and y, with ju > 1 and (/A — l)(v — k) 7* (k — ju) such that the following assumptions hold. (I) Every block is on k points, and every two intersecting blocks are on p. common...
متن کاملOn Sets with Few Intersection Numbers in Finite Projective and Affine Spaces
In this paper we study sets X of points of both affine and projective spaces over the Galois field GF(q) such that every line of the geometry that is neither contained in X nor disjoint from X meets the set X in a constant number of points and we determine all such sets. This study has its main motivation in connection with a recent study of neighbour transitive codes in Johnson graphs by Liebl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90067-1