We describe all finite-dimensional algebras A over an algebraically closed field for which the algebra of 2×2 upper triangular matrices over A is of tame representation type. Moreover, the algebras A for which is of polynomial growth (respectively, domestic, of finite representation type) are also characterized.
In this paper, we study the structure of group rings by means of endomorphism rings of their modules. The main tools used here, are the subrings fixed by automorphisms and the converse of Schur's lemma. Some results are obtained on fixed subrings and on primary decomposition of group rings.
We describe the images of multilinear polynomials of arbitrary degree evaluated on the upper triangular matrix algebra over an infinite field.