Rings with canonical reduction

2017/12/03 by Rahimi, Mehran
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.00755

Abstract

The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, (R, \mathfrakm) say, possessing a canonical ideal K which is a reduction of \mathfrakm. 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.

Related

• The reduction number of canonical ideals
• When is \mathfrakm:\mathfrakm an almost Gorenstein ring?
• Almost Gorenstein rings - towards a theory of higher dimension -
• Invariants of Cohen-Macaulay rings associated to their canonical ideals
• On the canonical ideals of one-dimensional Cohen-Macaulay local rings