Embedding a graded matrix algebra into an elementary graded

Abstract

M.V. Zaicev and S.K. Segal, as well as S. Dăscălescu, B. Ion, C. Năstăsescu, and D. Raios Montes studied certain gradings on matrix rings and algebras - 'elementary' gradings. However, examples of gradings on a matrix ring that are not elementary are known. In the present article, we show that any subalgebra of a full matrix ring over an arbitrary graded division ring can be embedded in an elementary graded matrix ring.