Frobenius Full Matrix Algebras and Gorenstein Tiled Orders

Abstract

ABSTRACT For integers n ≥ 2, n × n full matrix algebras with structure systems are introduced in Fujita (2003) as a framework to study certain factor algebras of tiled orders. Such factor algebras of Gorenstein tiled orders are Frobenius full matrix algebras. In this article, we verify that for every integer n ≤ 7, the converse is true. For every integer n ≥ 8, we show that the converse is not true, that is, there are Frobenius n × n full matrix algebras having no corresponding Gorenstein tiled orders.