In this work we introduce generalized projective geometries which are a natural generalization of projective geometries over a field or ring K but also of other important geometries such as Grassmannian, Lagrangian or conformal geometry (see [3]). We also introduce the corresponding generalized polar geometries and associate to such a geometry a symmetric space over K. In the finite-dimensional...

In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this ...

This paper is the sequel of [2]. In [4], S. Zhang defined the canonical height of subvarieties of an abelian variety over a number field in terms of adelic metrics. In this paper, we generalize it to an abelian variety defined over a finitely generated field over Q. Our way is slightly different from his method. Instead of using adelic metrics directly, we introduce an adelic sequence and an ad...

Unlike the classical Brauer group of a field, Brauer-Grothendieck singular scheme need not be torsion. We show that there exist integral normal projective surfaces over large field positive characteristic with non-torsion group. In contrast, we demonstrate such examples cannot algebraic closure finite field.

Any set of σ-Hermitian matrices of size n×n over a field with involution σ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two concepts are based upon the same set of points, up to some notational differences. Mathematics Subject Classification (2000): 51B05, 15A57, 51A50

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

We study links between algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in Q. We decompose the motive of a non-singular projective threefold X with representable algebraic part of CH0(X) into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the Griffiths’ intermediate Jacobian J(X) when the ground field is C. In partic...

Let G be a (not necessarily finite) group and p a finite dimensional faithful irreducible representation of G over an arbitrary field; write ~p for p viewed as a projective representation. Suppose that p is not induced (from any proper subgroup) and that ~p~ is not a tensor product (of projective representations of dimension greater than 1 ). Let AT be a noncentral subgroup which centralizes al...

It is known that a linear two-weight code C over a finite field Fq corresponds both to a multiset in a projective space over Fq that meets every hyperplane in either a or b points for some integers a < b , and to a strongly regular graph whose vertices may be identified with the codewords of C . Here we extend this classical result to the case of a ring-linear code with exactly two nonzero homo...

We address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular we derive that in any local ring R of mixed...