Geodesic
On the Krull property in topological algebras
Commentationes Mathematicae, Tome 46 (2006) no. 2, pp. 141-162.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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 \(Q'\)-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.
DOI : 10.14708/cm.v46i2.5213
Mots-clés : Krull algebra, annihilator algebra, semisimple algebra, socle, \(Q'\)-algebra, (D)-algebra, (weakly) regular annihilator algebra, (ortho)complemented algebra 
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Marina Haralampidou. On the Krull property in topological algebras. Commentationes Mathematicae, Tome 46 (2006) no. 2, pp.  141-162. doi : 10.14708/cm.v46i2.5213. http://geodesic.mathdoc.fr/articles/10.14708/cm.v46i2.5213/

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