A characterisation of local \(N\)-rings and an application to abstract harmonic analysis. (English) Zbl 1530.13016

Summary: A commutative ring with unity is called an \(N\)-ring if each of its ideals is contracted from a Noetherian extension ring. The chief result of this paper is a characterisation of local \(N\)-rings by their subdirectly irreducible quotients. The results are applied to characterise spectral synthesis on \(G\)-invariant subspaces of the space of complex valued functions on an abelian group \(G\).


13B30 Rings of fractions and localization for commutative rings
43A45 Spectral synthesis on groups, semigroups, etc.
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