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.

中文翻译：

---

Ulrich 理想和 2-AGL 环

2-almost Gorenstein局部环（简称2-AGL环）的概念是从典型理想的Sally模的角度对几乎Gorenstein局部环的概念的推广。在本文中，为了理论的进一步发展，我们讨论了 2-AGL 环的三个不同主题。第一个是阐明规范理想的最小表示的结构，第二个是研究某些纤维产品何时是 2-AGL 环的问题，所谓的合并重复。我们还探索了 2-AGL 环中的 Ulrich 理想，主要是两个生成的环。