Ascent and descent of Artinian module structures under flat base changes

Abstract

Let $\phi :R\to S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between R and S are investigated. For an Artinian R-module A, the structure of $A{\otimes }_{R}S$ is described. As an application, the Artinianess of certain local cohomology modules is clarified.

KEYWORDS:

• Artinian module
• ascent and descent of module structure
• flat extension
• local cohomology module

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13B40
• 13E10
• 13E05
• 13D45

Additional information

Funding

The work is supported by the Vietnam Ministry of Education and Training under grant number B2022-TNA-25.