Rings with canonical reduction

Abstract: The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \mathfrak{m})$ say, possessing a canonical ideal $K$ which is a reduction of $\mathfrak{m}$. We call $R$ to have canonical reduction $K$. We show that the class of rings with canonical reductions contains the class of almost Gorenstein rings and establish its relation with rings obtained by idealizations and also with numerical semigroup rings.