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Commutative Algebra I
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A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.Abstract:
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 typedread more
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Posted Content
Applications of Differential Graded Algebra Techniques in Commutative Algebra
TL;DR: Differential graded (DG) algebras are powerful tools from rational homotopy theory and as discussed by the authors survey some recent applications of these in the realm of homological commutative algebra.
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Minimal pairs, truncations and diskoids
TL;DR: In this article, the authors build on the correspondence between abstract key polynomials and minimal pairs made by Novacoski and show how to relate the valuations that are generated by each object.
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Root Extensions and Factorization in Affine Domains
TL;DR: In this article, it was shown that the ascent and descent of the IDPF property and atomicity for the pair of integral domains is governed by the relative sizes of the unit groups and whether the ring extension is a root extension or radical extension.
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Irreducible components of varieties of representations: the acyclic case
TL;DR: In this paper, the authors identify the irreducible components of affine components of the affine varieties of a quiver and describe the representations encoded by the components, including minimal projective presentations, generic sub-and quotient modules, etc.
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Topological properties of semigroup primes of a commutative ring
TL;DR: In this article, the authors studied the spectral properties of the space of prime semigroups of a commutative ring R under a natural topology introduced by B. Olberding.
References
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Book
Introduction to Commutative Algebra
TL;DR: It is shown here how the Noetherian Rings and Dedekind Domains can be transformed into rings and Modules of Fractions using the following structures: