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

Abstract

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 $G$.