A CHARACTERISATION OF LOCAL N-RINGS AND AN APPLICATION TO ABSTRACT HARMONIC ANALYSIS

Abstract

A BSTRACT . A commutative ring with unity is called an N -ring if each of its ideals is contracted from an Noetherian extension ring. The chief result of the 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 .