We consider digital expansions in lattices with endomorphisms acting as base. We focus on the w-non-adjacent form (w-NAF), where each block of w consecutive digits contains at most one non-zero digit. We prove that for su ciently large w and an expanding endomorphism, there is a suitable digit set such that each lattice element has an expansion as a w-NAF. If the eigenvalues of the endomorphism...

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that...

Let R be an associative ring with non-zero identity. For a Serre subcategory C of the category R-mod of left R-modules, we consider the class AC of all modules that do not belong to C, but all of their proper submodules belong to C. Alongside of basic properties of such associated classes of modules, we will prove that every uniform module of AC has a local endomorphism ring. Moreover, if R is ...