On -Cogenerated Commutative Unital -Algebras | Zendy

Ehsan Momtahan | Zendy

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On -Cogenerated Commutative Unital -Algebras

Author(s) -

Ehsan Momtahan

Publication year - 2013

Publication title -

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

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