In this paper, we introduce a new homological invariant called quasi-projective dimension, which is generalization of projective dimension. We discuss various properties Among other things, prove the following. (1) Over quotient regular local ring by sequence, every finitely generated module has finite (2) The Auslander--Buchsbaum formula and depth for modules dimension remain valid (3) Several...

Weyl modules play a central role in the representation theory of the general and special linear groups. There has been great interest recently in the modular case of these groups over fields of prime characteristic p. In particular, Glover [l] has proved some remarkable and comprehensive results about these modules for SL(2,p). We shall extend one of these theorems to the case of SL(2, q) where...

A standard associative graded algebra R over a field k is called Koszul if k admits a linear resolution as an R-module. A (right) R-module M is called Koszul if it admits a linear resolution too. Here we study a special class of Koszul algebras — roughly say, algebras having a lot of Koszul cyclic modules. Commutative algebras with similar properties (so-called algebras with Koszul filtrations)...

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category Cm(A) of A is the m-left part Lm(A (m)) of the m-replicated algebra of A. Moreover, we obtain a one-toone correspondence between the tilting objects in Cm(A) (that is, the m-clusters) and those tilting modules in modA(m) for which all non projective-injective di...

let $mathcal{x}$ be a class of $r$-modules‎. ‎in this paper‎, ‎we investigate ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective (projective) complexes which are generalizations of injective (projective) and dg-injecti‎‎ve (projective) complexes‎. ‎we prove that some known results can be extended to the class of ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective ...

We consider converses to the density theorem for square-integrable, irreducible, projective, unitary group representations restricted lattices using dimension theory of Hilbert modules over twisted von Neumann algebras. show that restriction such a σ-projective representation π unimodular, second-countable G lattice Γ extends module algebra (Γ,σ). then compute center-valued this module. For abe...