We revisit, clarify, and generalise classical results of Dickson (much later) Wagner on minimal Sym(n)- Alt(n)-modules. present a new, natural notion ‘modules with an additive dimension’ covering at once the classical, finitary case as well modules definable in o-minimal or finite Morley rank setting; this context, we fully identify faithful Alt(n)-modules least dimension.

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

By properly specializing the parameters irreducible modules of maximal dimension for the De Concini-Kac version of the Drinfeld-Jimbo quantum algebra in type A may be transformed into modules over Lusztig’s infinitesimal quantum algeba. Thus obtained modules have a simple socle and a simple head, and share the same dimension as the infinitesimal Verma modules. Despite these common features we f...