Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009 by Gunnar Fløystad, Trygve Johnsen, Andreas Leopold Knutsen
English | PDF | 2011 | 186 Pages | ISBN : 3642194915 | 2.6 MB
The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field.

Approximation Theorems in Commutative Algebra: Classical and Categorical Methods by J. Alajbegović , J. Močkoř
English | PDF | 1992 | 339 Pages | ISBN : 0792319486 | 43.3 MB
Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc.

A Singular Introduction to Commutative Algebra by Gert-Martin Greuel , Gerhard Pfister
English | PDF(True) | 2002 | 601 Pages | ISBN : 3540428976 | 46 MB
In theory there is no difference between theory and practice. In practice there is. Yogi Berra A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to commutative algebra and, at the same time, provides algorithms and computational practice. In this book, we do not separate the theoretical and the computational part. Coincidentally, as new concepts are introduced, it is consequently shown, by means of concrete examples and general proce dures, how these concepts are handled by a computer. We believe that this combination of theory and practice will provide not only a fast way to enter a rather abstract field but also a better understanding of the theory, showing concurrently how the theory can be applied. We exemplify the computational part by using the computer algebra sys tem SINGULAR, a system for polynomial computations, which was developed in order to support mathematical research in commutative algebra, algebraic geometry and singularity theory. As the restriction to a specific system is necessary for such an exposition, the book should be useful also for users of other systems (such as Macaulay2 and CoCoA) with similar goals. Indeed, once the algorithms and the method of their application in one system is known, it is usually not difficult to transfer them to another system.

A Singular Introduction to Commutative Algebra, Second, Extended Edition by Gert-Martin Greuel , Gerhard Pfister
English | PDF(True) | 2008 | 703 Pages | ISBN : 3540735410 | 9.9 MB
From the reviews of the first edition:

Chain Conditions in Commutative Rings
English | 2022 | ISBN: 3031098978 | 533 Pages | PDF EPUB (True) | 25 MB
This book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.

Markus Spitzweck, "A Commutative P1-spectrum Representing Motivic Cohomology over Dedekind Domains"
English | ISBN: 2856298907 | 2018 | 114 pages | PDF | 1 MB
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English | 2021 | ISBN: 0367700816 | 287 pages | True PDF | 11.37 MB
This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful.
Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability.

Computational Linear and Commutative Algebra by Martin Kreuzer
English | PDF(True) | 2016 | 332 Pages | ISBN : 331943599X | 2.8 MB
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving.