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arXiv · 2308.14842

Ring homomorphisms and local rings with quasi-decomposable maximal ideal

Saeed Nasseh·Keri Ann Sather-Wagstaff·Ryo Takahashi
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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 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.

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Saeed Nasseh, Keri Ann Sather-Wagstaff, Ryo Takahashi. 2023-08-28. Ring homomorphisms and local rings with quasi-decomposable maximal ideal. https://arxiv.org/abs/2308.14842

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