This result has been generalized in various directions, e.g. replacing the ground ring Z by a more general ring and dropping the cardinal restriction (in Corner’s result this is actually |A| < 20), see [2], [20], [8], [9], [4], [23]. Other extensions include abelian groups which are not necessarily torsionfree, see Corner, Göbel [4] for references. Here we are interested in a different strength...

Let p > 2 be a prime, The group ring RG is calculated nearly up to Morita equivalence: The projections of RG into the simple components of KG are given explicitly and the endomorphism rings and homomorphism bimodules between the projective indecomposable RG-lattices are described.

We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can be adapted to yield the discriminant of the endomorphism ring of the curve.

Let Fq be the finite field with q elements, A := Fq[T ] and F := Fq(T ). Let φ be a Drinfeld A-module over F with trivial endomorphism ring. We prove analogues of the Erdös and Halberstam Theorems for φ. If φ has rank ≥ 3, we assume the validity of the Mumford-Tate Conjecture for φ. 1

For a self-small abelian group A of torsion-free rank 1, we characterize A-reflexive abelian groups which are induced by the contravariant functor Hom(−, A) in two cases: the range of Hom(−, A) is the category of all abelian groups, respectively the range of Hom(−, A) is the category of all left E-modules, where E is the endomorphism ring of A.

We study the quasi-endomorphism ring of certain infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a MordellLang theorem for Drinfeld modules of finite characteristic. Using specialization arguments we prove also a Mordell-Lang theorem for Drinfeld modules of generic characteristic.

For any equivalence relation ≡ on positive integers such that nk ≡ mk if and only if n ≡ m, there is an abelian group G such that the endomorphism ring of Gn and Gm are isomorphic if and only if n ≡ m. However, Gn and Gm are not isomorphic if n = m.

We prove that every stable, combinatorial model category can be enriched in a natural way over symmetric spectra. As a consequence of the general theory, every object in such a model category has an associated homotopy endomorphism ring spectrum. Basic properties of these invariants are established.

In this paper, we study the fundamental algorithmic problem of determining the homomorphisms from an Amodule M to an A-module N over an algebra A. We shall outline an algorithm for the case that A is a finite dimensional algebra over a finite field F and both modules M and N are finitely generated as A-modules. More specifically, the input to our algorithm consists of the following data: The mo...

We describe a novel technique to handle big permutation domains for large groups. It is applied to the multiplicity-free action of the sporadic simple Baby Monster group on the cosets of its maximal subgroup Fi23, to determine the character table of the associated endomorphism ring.