Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by SubV (resp., EndV ) the collection of all subspaces (resp., endomorphisms) of a vector space V . We prove various results that imply the following: (1) If cardΩ > 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff card Γ > 2 . In particular, if Ω has at least two elements, th...

The notion of ring endomorphisms having large images is introduced. Among others, injectivity and surjectivity of such endomorphisms are studied. It is proved, in particular, that an endomorphism σ of a prime one-sided noetherian ringR is injective whenever the image σ(R) contains an essential left ideal L of R. If additionally σ(L) = L, then σ is an automorphism of R. Examples showing that the...

A Hecke endomorphism algebra is a natural generalisation of the qSchur algebra associated with the symmetric group to a Coxeter group. For Weyl groups, Parshall, Scott and the first author [9, 10] investigated the stratification structure of these algebras in order to seek applications to representations of finite groups of Lie type. In this paper we investigate the presentation problem for Hec...