On the Krull property in topological algebras

• Autorzy: Marina Haralampidou
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Krull algebra; annihilator algebra; semisimple algebra; socle; \(Q'\)-algebra; (D)-algebra; (weakly) regular annihilator algebra; (ortho)complemented algebra

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2006
• Tom: 46
• Numer: 2

Daty

wydano

2006

online

2017-12-19

Twórcy

autor

Marina Haralampidou

Identyfikatory

DOI

10.14708/cm.v46i2.5213