# 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

## 2,058 Citations

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

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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.

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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…

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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…

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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…

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## References

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* 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

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

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### 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
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### Commutative algebra, volume 150 of Graduate Texts in Mathematics

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