Quasi-hereditary algebras arise in several natural contexts. For example, their module categories often appear in connection with the representation theory of algebraic groups over elds of positive characteristic or of quantum groups at a root of unity. This point of view has been exploited by various authors, e. g., [CPS3{8], [G2], etc. Classical Schur algebras attached to the general linear g...

We present a Mordell-Lang statement for Drinfeld modules. In the case of Drinfeld modules of finite characteristic, we show the connection between our Mordell-Lang statement and the study of the ring of quasi-endomorphisms for a certain minimal group in the theory of separably closed fields associated to the Drinfeld module.

If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we prove that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.

In this note we settle some technical questions concerning finite rank quasi-free Hilbert modules and develop some useful machinery. In particular, we provide a method for determining when two such modules are unitarily equivalent. Along the way we obtain representations for module maps and study how to determine the underlying holomorphic structure on such modules.

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

It is considered a smooth projective morphism p : T ! S to a smooth variety S. It is proved, in particular, the following result. The total direct image Rp (Z=nZ) of the constant etale sheaf Z=nZis locally for Zarisky topology quasi-isomorphic to a bounded complex L on S consisting of locally constant constructible etale Z=nZ-module sheaves.

A numerical procedure for extracting parasitic circuit elements using a quasi-static field solver, as part of the Virtual Test Bed (VTB), is discussed. The parasitic inductance and capacitance values obtained from the model are compared to measured values from a low-inductance Power Electronic Building Block (PEBB) module, designed and constructed at Harris Semiconductor.

A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of m-harmonic polynomials, thus the earlier results of Veselov and the author for the case of constant multiplicity are generalized.

0. Introduction. This paper continues the study of the noncommutative innn-itesimal cohomology we introduced in 3]. This is the cohomology of sheaves on a noncommutative version of the commutative innnitesimal site of Grothendieck ((8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the innnitesimal site gives de Rham cohomol-og...