میر سجاد هاشمی

We extend the notion of homomorphisms and characters to n -homomorphisms and n -characters on algebras, and then show that some properties of characters are also valid for n -characters on commutative lmc topological algebras, and the space of continuous n -characters M(A,n) is relatively compact in A′ (the dual space of A ), with the weak* topology (Gelfand topology), whenever A is a commutative lmc Q -algebra. We also find relations between characters, n -characters, and continuous n -characters on commutative Fréchet algebras. Let B be a topological algebra and (Aα,φβα) (resp. (Aα,φαβ) ) be an inductive system (resp. a projective system) of topological algebras. Then we obtain relations between n−Hom(Aα,B) and n−Hom(A,B) , or between Open image in new window, the inductive limit, and M(A,n) , where Open image in new window, is the inductive limit (resp. A=lim←−Aα , is the projective limit) and n−Hom(Aα,B) (resp. n−Hom(A,B) ), is the space of all continuous n-homomorphisms from Aα (resp. A ) into B .