The structure of chains of Ulrich ideals in Cohen-Macaulay local rings of dimension one

2018/04/18 by Goto, Shiro, Isobe, Ryotaro, Kumashiro, Shinya
#13H10 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.06643

Abstract

This paper studies Ulrich ideals in one-dimensional Cohen-Macaulay local rings. A correspondence between Ulrich ideals and overrings is given. Using the correspondence, chains of Ulrich ideals are closely explored. The specific cases where the rings are of minimal multiplicity and GGL rings are analyzed.

Related

• Ulrich ideals and almost Gorenstein rings
• Ulrich ideals and modules
• Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity
• Non-existence of Ulrich modules over Cohen-Macaulay local rings
• Ulrich split rings