Ulrich ideals and 2-AGL rings
Shiro Goto, Ryotaro Isobe, and Naoki Taniguchi
TL;DR
This paper explores the structure and properties of 2-almost Gorenstein local rings, focusing on canonical ideals, fiber product constructions, and Ulrich ideals, to advance the understanding of their algebraic characteristics.
Contribution
It provides new insights into the structure of canonical ideals, conditions for fiber products to be 2-AGL rings, and the nature of Ulrich ideals within these rings.
Findings
Clarified the structure of minimal presentations of canonical ideals.
Identified conditions under which fiber products are 2-AGL rings.
Analyzed properties of two-generated Ulrich ideals in 2-AGL rings.
Abstract
The notion of 2-almost Gorenstein local ring (2-AGL ring for short) is a generalization of the notion of almost Gorenstein local ring from the point of view of Sally modules of canonical ideals. In this paper, for further developments of the theory, we discuss three different topics on 2-AGL rings. The first one is to clarify the structure of minimal presentations of canonical ideals, and the second one is the study of the question of when certain fiber products, so called amalgamated duplications are 2-AGL rings. We also explore Ulrich ideals in 2-AGL rings, mainly two-generated ones.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras