Open AccessOn -Cogenerated Commutative Unital -Algebras
Author(s) -
Ehsan Momtahan
Publication year - 2013
Publication title -
algerba/algebra
Language(s) - English
Resource type - Journals
eISSN - 2314-4114
pISSN - 2314-4106
DOI - 10.1155/2013/452862
Subject(s) - mathematics , commutative property , unital , intersection (aeronautics) , separable space , pure mathematics , simple (philosophy) , space (punctuation) , zero (linguistics) , characterization (materials science) , discrete mathematics , algebra over a field , mathematical analysis , philosophy , linguistics , epistemology , engineering , aerospace engineering , materials science , nanotechnology
Gelfand-Naimark's theorem states that every commutative -algebra is isomorphic to a complex valued algebra of continuous functions over a suitable compact space. We observe that for a completely regular space , is dense--separable if and only if is -cogenerated if and only if every family of maximal ideals of with zero intersection has a subfamily with cardinal number less than and zero intersection. This gives a simple characterization of -cogenerated commutative unital -algebras via their maximal ideals