In this note we prove: If a subdirect product of ̄nitely many ̄nite projective geometries has the cover-preserving embedding property, then so does each factor. In what follows all the lattices will be ̄nite modular ones. A ̄nite lattice K has the cover-preseving embedding property, abbreviated as CPEP with respect a variety V of lattices if whenever K can be embedded into a ̄nite lattice L in ...

Let Λ be a finite dimensional algebra over an algebraically closed field, and S a finite sequence of simple left Λ-modules. Quasiprojective subvarieties of Grassmannians, distinguished by accessible affine open covers, were introduced by the authors for use in classifying the uniserial representations of Λ having sequence S of consecutive composition factors. Our principal objectives here are t...

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

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quas...

Let R be a ring and M a right R-module. M is called n-FP-projective if Ext M N = 0 for any right R-module N of FP-injective dimension ≤n, where n is a nonnegative integer or n = . R M is defined as sup n M is n-FP-projective and R M = −1 if Ext M N = 0 for some FP-injective right R-module N. The right -dimension r -dim R of R is defined to be the least nonnegative integer n such that R M ≥ n im...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theorem for these stratifications in terms of complex tori and convex rational polytopes, generalizing to the quas...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...