We introduce Krull topological algebras. In particular, we characterize the Krull property in some special classes of topological algebras. Connections with the theory of semisimple annihilator Q0-algebras are given. Relative to this, an investigation on the relationship between Krull and (weakly) regular (viz. modular) annihilator algebras is considered. Subalgebras of certain Krull algebras are also presented. Moreover, conditions are supplied under which the Krull (resp. Q'-) property is preserved via algebra morphisms. As an application, we show that the quotient of a Krull Q'-algebra, modulo a 2-sided ideal, is a topological algebra of the same type. Finally, we study the Krull property in a certain algebra-valued function topological algebra.
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We classify certain locally m-convex algebras, in terms of Le Page condition. In particular, we show that a unital locally m-convex algebra E satisfies Le Page condition and has no non-trivial idempotents if and only if E = C , within a topological algebra isomorphism. Besides, the algebra Cm<-E^ ( pointwise defined operations and cartesian product topology) characterizes all complex unital complete locally m-convex Le Page Q'-algebras E which have a discrete spectrum VJl(E). Hence, the algebra in question is not finite dimensional, by contrast with the classical case, where a unital complex Banach algebra satisfying Le Page condition is finite dimensional. The first principal Wedderburn structure theorem, for certain particular locally m-convex algebras satisfying the generalized Le Page condition is obtained.
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