The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce topics of current research, centered around the themes of Gröbner bases, resultants and syzygies.
There are natural instances however, where the assumptions of Theorem 2.9 are satisfied, despite some bad behavior of the Koszul homology modules. I am grateful to Mark Johnson for pointing out to me the following example ...
We define a divisor ( or Weil divisor ) in any ring R to be an element of the free abelian group Div ( R ) whose generators are the codimension 1 prime ideals of R. That is , a Weil divisor of R is a formal linear combination of ...
... 576 Apéry, R., 542 apparently silly definition, 506 approximate root, 183, 209 Arabic, article in, 576 Artin, E., ... N., 576 branch of a plane curve, 129, 185 Brieskorn, E., 515 Brouwer, L.E.J., 214 Bruhat decomposition, 369 Bruns, ...
The purpose of this book is twofold: to present some basic ideas in commutative algebra and algebraic geometry and to introduce topics of current research, centered around the themes of Gröbner bases, resultants and syzygies.
Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions Marco Fontana, Sophie Frisch, ... Recent progress in coherent rings: a homological perspective, in Progress in Commutative Algebra 1 (De Gruyter, ...
Morey, S. and Villarreal, R. Edge ideals: algebraic and combinatorial properties, Progress in commutative algebra 1, 85–126, de Gruyter, Berlin, 2012. 103. Murai, S. and Hibi, T. Algebraic shifting and graded Betti numbers, Trans. Amer.
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra.
This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage.
The central theme of this volume is commutative algebra, with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra.
... Wolmer V. Vasconcelos, Divisor theory in module categories, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1974. North-Holland Mathematics Studies, No. 14; Notas de Matemática No.
M. Hochster, Canonical elements in local cohomology modules and the Direct Summand Conjecture, J. Algebra 84 ... W.V. Vasconcelos, Divisor theory in Module Categories, Mathematics Studies 14, North-Holland, Amsterdam-Oxford, 1973.
This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'.
This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra.
This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage.
Commutative Algebra
... phantom homology . = The proof of Theorem 6.3 is based on a " constructive " reformulation of the Buchsbaum - Eisenbud acyclicity theorem . To establish notation , let G. = ( 6.4 ) 0 → Gn On , 1 Go Gn - 1 be a complex of finitely ...