The Trivial Extension of SAG-Algebra

Abstract

    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 .