$n$-ideal and $n$-weak amenability of Frechet algebras

Abstract: In this paper, we introduce and study some notations of amenability such as $n$-ideal amenability and $n$-weak amenability for Frechet algebra and we examine how these concepts in Banach algebra can be generalized and defined for Frechet algebra. We will also examine some inherited properties of $n$-ideal and $n$-weak amenable Frechet algebra and determine the relations between $m$ and $n$-weak amenability and $m$ and $n$-ideal amenability for Frechet algebra. Also, the relation of these new concepts of amenability of a Frechet algebra and its unitization is investigated.