A family of quotients of the Rees algebra
Valentina Barucci, Marco D'Anna, Francesco Strazzanti
TL;DR
This paper introduces a new family of quotient rings derived from the Rees algebra, unifying classical idealization and amalgamated duplication concepts, and explores their shared properties.
Contribution
It generalizes existing constructions of quotient rings from the Rees algebra, revealing properties common to the entire family.
Findings
Several properties are invariant across the family
The family unifies idealization and amalgamated duplication
New insights into the structure of quotient rings from Rees algebra
Abstract
A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Commutative Algebra and Its Applications