Commutative Algebra I

@inproceedings{Huneke2012CommutativeAI,
  title={Commutative Algebra I},
  author={Craig Huneke},
  year={2012}
}
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed 

Complexity Degrees of Algebraic Structures

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of

Chordal and Complete Structures in Combinatorics and Commutative Algebra

This thesis is divided into two parts. The first part is concerned with the commutative algebra of certain combinatorial structures arising from uniform hypergraphs. The main focus lies on two part

Computing upper cluster algebras

This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is

PURE SUBRINGS OF COMMUTATIVE RINGS

We study subalgebras $A$ of affine or local algebras $B$ such that $A{\hookrightarrow}B$ is a pure extension from algebraic and geometric viewpoints.

Incidence systems on Cartesian powers of algebraic curves

We show that a reduct of the Zariski structure of an algebraic curve which is not locally modular interprets a field, answering a question of Zilber's.

On the Structure of Graded Commutative Exponential functors

  • Antoine Touz'e
  • Mathematics
    International Mathematics Research Notices
  • 2019
We investigate the structure of graded commutative exponential functors. We give applications of these structure results, including computations of the homology of the symmetric groups and of

Seven lectures on universal algebraic geometry

  • B. Plotkin
  • Mathematics
    Groups, Algebras and Identities
  • 2019
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions

CHARACTERISTIC POLYNOMIALS OF CENTRAL SIMPLE ALGEBRAS

We characterize characteristic polynomials of elements in a central simple algebra. We also give an account for the theory of rational canonical forms for separable linear transformations over a

Symbolic Rees Algebras

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a
...

References

SHOWING 1-5 OF 5 REFERENCES

Introduction to commutative algebra

* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *

An algebraic introduction to complex projective geometry. 1, volume 47 of Cambridge Studies in Advanced Mathematics

  • Commutative algebra
  • 1996

Commutative algebra, volume 150 of Graduate Texts in Mathematics With a view toward algebraic geometry

  • Commutative algebra, volume 150 of Graduate Texts in Mathematics With a view toward algebraic geometry
  • 1995

An algebraic introduction to complex projective geometry. 1, volume 47 of Cambridge Studies in Advanced Mathematics Commutative algebra

  • An algebraic introduction to complex projective geometry. 1, volume 47 of Cambridge Studies in Advanced Mathematics Commutative algebra
  • 1996

Commutative algebra, volume 150 of Graduate Texts in Mathematics

  • 1995