2023/08/28 by Saeed Nasseh, Nasseh, Saeed, Keri Ann Sather‐Wagstaff +3 · 1 citation
Computer Science · Mathematics · #13D02 #13D05 #13D07 #13H10 #18A30 #Advanced Algebra and Logic #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2308.14842
openalex publication_date 2023/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 show 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.