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On algebras of bounded continuous functions valued in a topological algebra

Arizmendi-Peimbert H., Chō M., Garcia A.

Commentationes Mathematicae

2017

Vol 57, No. 2

123--129

Let X be a completely regular space. We denote by C(X,A) the locally convex algebra of all continuous functions on X valued in a locally convex algebra A with a unit e. Let Cb(X,A) be its subalgebra consisting of all bounded continuous functions and endowed with the topology given by the uniform seminorms of A on X. It is clear that A can be seen as the subalgebra of the constant functions of Cb(X,A). We prove that if A is a Q-algebra, that is, if the set G(A) of the invertible elements of A is open, or a Q-álgebra with a stronger topology, then the same is true for Cb(X,A).

On the Krull property in topological algebras

Haralampidou M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

141-162

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.

Some characterizations of Q-algebras

Arizmendi H.P., Valov V.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1999

[Z] 39

11-21

We characterize topological Q-algebras and generalizations of Q-algebras. Some applications of our results are given.