A family of quotients of the Rees Algebra
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In this article, a family of quotient rings of the Rees algebra associated to a commutative ring is studied, which generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring.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.read more
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One-dimensional Gorenstein local rings with decreasing Hilbert function
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On n-Trivial Extensions of Rings
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Families of Gorenstein and almost Gorenstein rings
TL;DR: In this article, it was shown that the Nagata idealization and amalgamated duplication properties depend only on a commutative ring and an ideal ring, and not on the whole Rees algebra.
References
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Book
Integral closure of ideals, rings, and modules
Craig Huneke,Irena Swanson +1 more
TL;DR: In this paper, the authors define the integral closure of rings and define a table of basic properties including separation, separationability, separation of rings, and normal homomorphisms, and the Briancon-Skoda theorem.
Journal ArticleDOI
An amalgamated duplication of a ring along an ideal: the basic properties
Marco D'Anna,Marco Fontana +1 more
TL;DR: In this article, the authors introduce a general construction, denoted by R ⋈ E, called the amalgamated duplication of a ring R along an R-module E, that they assume to be an ideal in some overring of R.
Journal ArticleDOI
A construction of Gorenstein rings
TL;DR: In this article, a commutative ring R and a proper ideal I ⊂ R were constructed and a new ring denoted by R⋈I was studied.