TL;DR
This paper introduces the concept of Ratliff-Rush closure for modules, investigates its relation to integral closure, and characterizes this relation via the normality of the Rees algebra's projective scheme, extending previous results.
Contribution
It generalizes the characterization of Ratliff-Rush closure for modules and provides criteria for Buchsbaum Rees algebras, expanding the understanding of module closures.
Findings
Ratliff-Rush closure of modules is characterized by the normality of the Rees algebra's projective scheme.
The paper generalizes previous results relating to the integral closure and Ratliff-Rush closure.
Provides a criterion for Buchsbaum Rees algebras.
Abstract
In this paper, we introduce the notion of Ratliff-Rush closure of modules and explore whether the condition of the Ratliff-Rush closure coincides with the integral closure. The main result characterizes the condition in terms of the normality of the projective scheme of the Rees algebra, which generalizes the result of S. Goto and N. Matsuoka. In conclusion, we shall give a criterion for the Buchsbaum Rees algebras.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras