A note on noetherianity. (French) Zbl 1199.46113

Choukri, R.; El Kinani, A.; Oukhouya, A.

Mat. Vesn. 60, No. 1, 53-57 (2008).

The authors show that a commutative unitary Banach algebra in which all maximal ideals are of finite type is a noetherian algebra, hence of finite dimension. Concerning l.m.c. commutative unitary Fréchet algebras, they derive certain properties of maximal ideals of such algebras in the case that they are not noetherian.

Reviewer: Zoran Kadelburg (Beograd)

MSC:

46J10	Banach algebras of continuous functions, function algebras
46J20	Ideals, maximal ideals, boundaries

Keywords:

noetherian algebra; l.m.c. algebra; maximal ideal