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Publication

The multivariate Serre conjecture ring

Luc Guyot
2023
Journal Articles

Abstract

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Official source

https://infoscience.epfl.ch/entities/publication/1f6cfe27-bcc8-4186-80d6-ded19479f26f

About this result

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Luc Guyot
2023
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/1f6cfe27-bcc8-4186-80d6-ded19479f26f

About this result

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Related concepts (31)

Polynomial ring

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers.

Finitely generated module

In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.

Monic polynomial

In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1. That is to say, a monic polynomial is one that can be written as with Monic polynomials are widely used in algebra and number theory, since they produce many simplifications and they avoid divisions and denominators. Here are some examples. Every polynomial is associated to a unique monic polynomial.

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