On -Cogenerated Commutative Unital -Algebras
Keyword(s):
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.
2013 ◽
Vol 2013
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pp. 1-6
Keyword(s):
Keyword(s):
1960 ◽
Vol 12
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pp. 353-362
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1975 ◽
Vol 19
(3)
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pp. 221-229
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Keyword(s):
1989 ◽
Vol 39
(3)
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pp. 353-359
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1987 ◽
Vol 29
(1)
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pp. 65-68
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1959 ◽
Vol 3
(1)
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pp. 121-133
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