This paper is a survey about ring theory properties of some quotients of Rees algebras Rf(i), where R is a unitary commutative ring, f ∈ R[T] and i is an ideal of R. More precisely Rf(i) := R[iT]/(fR[T] ∩ R[iT]). These rings can be studied using pullback constructions (this is very useful to describe the prime spectrum and to investigate some questions related to the structure of the ideals). We start by discussing the case when the polynomial f has degree 2 and in the last section we generalize to constructions obtained with polynomials of any degree
Finocchiaro, C.A., Tartarone, F. (2025). On a class of quotients of Rees algebras: a survey. In Recent progress in ring and factorization theory (pp.229-239). Springer [10.1007/978-3-031-75326-8].
On a class of quotients of Rees algebras: a survey
Francesca Tartarone
2025-01-01
Abstract
This paper is a survey about ring theory properties of some quotients of Rees algebras Rf(i), where R is a unitary commutative ring, f ∈ R[T] and i is an ideal of R. More precisely Rf(i) := R[iT]/(fR[T] ∩ R[iT]). These rings can be studied using pullback constructions (this is very useful to describe the prime spectrum and to investigate some questions related to the structure of the ideals). We start by discussing the case when the polynomial f has degree 2 and in the last section we generalize to constructions obtained with polynomials of any degreeI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
