Stratifying algebras with near-matrix algebras

Given a left module U and a right module V over an algebra D and a D–D-bilinear form β:U×V→D, we may define an associative algebra structure on the tensor product V DU. This algebra is called a near-matrix algebra. In this paper, we shall investigate algebras filtered by near-matrix algebras in some nice way and give a unified treatment for quasi-hereditary algebras, cellular algebras, and stratified algebras.