Abstract
This chapter presents a study on certain ideals of holomorphic functions or holomorphic germs on infinite dimensional spaces/Fréchet spaces. The chapter discusses the ideal generated by a family of holomorphic functions without common zeros, and likewise for holomorphic germs. Throughout the chapter the finite dimensional result by Cartan is kept in mind. The chapter presents the establishment of some properties of certain classes of topological algebras. The chapter presents the collection of some results concerning approximation of holomorphic functicns by continuous polynomials. The chapter also discusses locally m-convex algebras and Q-algebras. By an algebra, a commutative complex algebra is meant with unit element. By a complex homomorphism on an algebra A an algebra homomorphism T: A → C is meant, which is not identically zero. A topological algebra is an algebra and a topological vector space such that ring multiplication is separatelycontinuous.
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