Segal Frechet algebras

Abstract: Let (A,p_l){l\in\Bbb N} be a Frechet algebra. In this paper, we introduce the concept of Segal Frechet algebra and investigate known results about abstract Segal algebras, for Segal Frechet algebras. Also we recall the concept of approximate identities for topological algebras and provide some remarkable results for Segal Frechet algebras. Moreover, we verify ideal theorem for Frechet algebras and characterize closed ideals of Segal Frechet algebra (B,q_m){m\in\Bbb N} in (A,p_l)_{l\in\Bbb N}.