Work

Ring homomorphisms and local rings with quasi-decomposable maximal ideal

Year: 2024

Type: article

Abstract: The notion of local rings with quasi-decomposable maximal ideal was formally introduced by Nasseh and Takahashi. In separate works, the authors of the present paper showed that such rings have rigid homological properties; for instance, they are both Ext- and Tor-friendly. One point of this paper is to further explore the homological properties of these rings and also introduce new classes of such rings from a combinatorial point of view. Another point is to investigate how far some of these homological properties can be pushed along certain diagrams of local ring homomorphisms.

Source: Communications in Algebra

DOI: 10.1080/00927872.2024.2345843

Authors: Saeed Nasseh, KeriAnn Sather-Wagstaff, Ryo Takahashi

Institutions: Georgia Southern University, Clemson University, Nagoya University

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Japan Society for the Promotion of Science

Awards: 各種の関数と次元による可換環の導来圏の研究, G6496167347