Geodesic
On Frobenius full matrix algebras with structure systems
Algebra and discrete mathematics, no. 1 (2007), pp. 24-39.

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Let $n\geq 2$ be an integer. In [5] and [6], an $n\times n$ $\mathbb A$-full matrix algebra over a field $K$ is defined to be the set $\mathbb M_n(K)$ of all square $n\times n$ matrices with coefficients in $K$ equipped with a multiplication defined by a structure system $\mathbb A$, that is, an $n$-tuple of $n\times n$ matrices with certain properties. In [5] and [6], mainly $\mathbb A$-full matrix algebras having (0,1)-structure systems are studied, that is, the structure systems $\mathbb A$ such that all entries are 0 or 1. In the present paper we study $\mathbb A$-full matrix algebras having non (0,1)-structure systems. In particular, we study the Frobenius $\mathbb A$-full matrix algebras. Several infinite families of such algebras with nice properties are constructed in Section 4.
Keywords: Frobenius algebra, quiver, tame representation type.
Mots-clés : module, socle 
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Hisaaki Fujita; Yosuke Sakai; Daniel Simson. On Frobenius full matrix algebras with structure systems. Algebra and discrete mathematics, no. 1 (2007), pp. 24-39. http://geodesic.mathdoc.fr/item/ADM_2007_1_a2/