Properties of TQ-algebras

TQ-algebrate omadusiTQ-algebrate Omadusi

Mati Abela ； Wiesław Zelazko

《Proceedings of the Estonian Academy of Sciences.Chemistry》 60卷3期 (2011/09) Pp. 141-148

摘要

On vaadeldud ühe-ja kahepoolsete TQ-algebrate ning ühe-ja kahepoolsete topoloogiliste ideaalide põhiomadusi. On esitatud näiteid TQ-algebratest ja sõnastatud mõned senini lahendamata probleemid.

並列摘要

Several properties of unital left (right) TQ-algebras are described. The conditions when a unital semitopological algebra is a left (right) TQ-algebra are given. It is shown that the space M (A) (of nontrivial continuous multiplicative linear functionals on A) in the Gelfand topology is a compact Hausdorff space for every unital TQ-algebra with a nonempty set M (A) and a commutative complete metrizable unital algebra is a TQ-algebra if and only if all maximal topological ideals of A are closed. Examples of TQ-algebras are given. Open problems are presented.

並列關鍵字

topological algebras ； Q-algebras ； TQ-algebras ； topological ideals