Descriptions of all closed maximal one-sided ideals in topological algebras

摘要

Let f: A → B be a homomorphism of topological algebras, I a closed maximal regular left (right) ideal of A and J a closed maximal regular left (right) ideal of B. We study under which conditions f(I) or f~(-1)(J) is a closed maximal regular left (right) ideal and the relationship between closed maximal regular left (right) ideals in A and B. Using these results, descriptions of all closed maximal regular one-sided ideals in topological algebras by primitive ideals and by extendible ideals are given.