The Trivial Extension of SAG-Algebra

The string almost gentle algebras (SAG-algebras) are studied in this paper. Generalizing the properties of string almost gentle algebras has also given. Let be the string almost gentle algebras, with quiver and admissible ideal of algebra. We show that the radical of string almost gentle algebras can be written as a direct sum of uniserial modules. After that the quiver is constructed from and an extension of the quiver is showed. Also, the quiver which is a quiver of trivial extension of string almost gentle algebras has been studied. Consequently, the relations of algebra have been described. As well as, we will show that the algebra is an extension to string almost gentle algebras. Furthermore, we describe the trivial extension of string almost gentle algebras , we prove and that the trivial extension of is isomorphic to the algebra .