000			02972nam a22003738i 4500
001			CR9780511608681
003			UkCbUP
005			20200124160218.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090910s1998||||enk o ||1 0|eng|d
020			_a9780511608681 (ebook)
020			_z9780521566742 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA251.38 _b.B78 1998
082	0	4	_a512.4 _221
100	1		_aBruns, Winfried, _d1946- _eauthor.
245	1	0	_aCohen-Macaulay rings / _cWinfried Bruns, Jürgen Herzog.
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c1998.
300			_a1 online resource (xiv, 453 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge studies in advanced mathematics ; _v39
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aRegular sequences and depth -- Cohen-Macaulay rings -- The canonical module. Gorenstein rings -- Hilbert functions and multiplicities -- Stanley-Reisner rings -- Semigroup rings and invariant theory -- Determinantal rings -- Big Cohen-Macaulay modules -- Homological theorems -- Tight closure -- Appendix: A summary of dimension theory.
520			_aIn the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.
650		0	_aCohen-Macaulay rings.
700	1		_aHerzog, Jürgen, _d1941- _eauthor.
776	0	8	_iPrint version: _z9780521566742
830		0	_aCambridge studies in advanced mathematics ; _v39.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511608681
999			_c516517 _d516515