Hecke endomorphism algebras are endomorphism algebras over a Hecke algebra associated to a finite Weyl group W of certain q-permutation modules, the “tensor spaces.” Such a space may be defined for any W in terms of a direct sum of certain cyclic modules associated to parabolic subgroups. The associated algebras have important applications to the representations of finite groups of Lie type. In...

It should be noted that the definition (introduced in [l]) of a normal endomorphism of a loop G is radically different from the usual definition for groups. Nevertheless (as shown in [2]) the two definitions are equivalent when G is a group. In particular, the present theorem generalizes one of Heerema [3]. We may add that in [2], by assuming that the loop G was Moufang, we were able to be much...

For any complete chain I whose distinct elements are separated by cover pairs, and for every family {Mi | i∈ I} of monoids, we construct a family of graphs {Gi | i∈ I} such that Gi is a proper induced subgraph of Gj for all i; j∈ I with i ¡ j, Gi = ⋂ {Gj | j∈ I; i ¡ j} whenever i = inf{ j∈ I | j¿ i} in I , Gi = ⋃ {Gj | j∈ I; j ¡ i} whenever i = sup{ j∈ I | j¡ i} in I , the endomorphism monoid o...

It is well-known that modules with pathological properties can be obtained by constructing modules with \nearly prescribed" endomorphism rings. (See, for example, [5], [2], [3], or [10].) Here we shall investigate that method using a rather weak notion of nearly prescribing the endomorphism ring, namely one that just requires that a certain ring be algebraically closed in the endomorphism ring ...