圖書標籤: 數學 代數 交換代數 Mathematics Algebra 其餘代數7 Commutative_Algebra Algebraic_Combinatorics
发表于2024-12-23
Cohen-Macaulay Rings pdf epub mobi txt 電子書 下載 2024
In 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.
交換代數的進階讀物,讀完大半本Matsumura後可以入手,前四章強化基本理論,第五章與組閤交換代數相銜接,此外還包括局部上同調,代數不變量理論、大Cohen-Macaulau模,tight closure等諸多領域的導引,此後不管往哪裏走都很方便的啊~
評分交換代數的進階讀物,讀完大半本Matsumura後可以入手,前四章強化基本理論,第五章與組閤交換代數相銜接,此外還包括局部上同調,代數不變量理論、大Cohen-Macaulau模,tight closure等諸多領域的導引,此後不管往哪裏走都很方便的啊~
評分交換代數的進階讀物,讀完大半本Matsumura後可以入手,前四章強化基本理論,第五章與組閤交換代數相銜接,此外還包括局部上同調,代數不變量理論、大Cohen-Macaulau模,tight closure等諸多領域的導引,此後不管往哪裏走都很方便的啊~
評分交換代數的進階讀物,讀完大半本Matsumura後可以入手,前四章強化基本理論,第五章與組閤交換代數相銜接,此外還包括局部上同調,代數不變量理論、大Cohen-Macaulau模,tight closure等諸多領域的導引,此後不管往哪裏走都很方便的啊~
評分交換代數的進階讀物,讀完大半本Matsumura後可以入手,前四章強化基本理論,第五章與組閤交換代數相銜接,此外還包括局部上同調,代數不變量理論、大Cohen-Macaulau模,tight closure等諸多領域的導引,此後不管往哪裏走都很方便的啊~
Stanley-Reisner环(又称为面环(face ring))把代数拓扑中单纯复形与多项式的单项商环联系起来,可以说是一张通向组合交换代数的入场券,下面就来介绍一下关于它的基本内容。 先看Stanley-Reisner环的定义,设k是作为系数的交换环,给定任何一个顶点集为{v_1,…,v...
評分Stanley-Reisner环(又称为面环(face ring))把代数拓扑中单纯复形与多项式的单项商环联系起来,可以说是一张通向组合交换代数的入场券,下面就来介绍一下关于它的基本内容。 先看Stanley-Reisner环的定义,设k是作为系数的交换环,给定任何一个顶点集为{v_1,…,v...
評分Stanley-Reisner环(又称为面环(face ring))把代数拓扑中单纯复形与多项式的单项商环联系起来,可以说是一张通向组合交换代数的入场券,下面就来介绍一下关于它的基本内容。 先看Stanley-Reisner环的定义,设k是作为系数的交换环,给定任何一个顶点集为{v_1,…,v...
評分Stanley-Reisner环(又称为面环(face ring))把代数拓扑中单纯复形与多项式的单项商环联系起来,可以说是一张通向组合交换代数的入场券,下面就来介绍一下关于它的基本内容。 先看Stanley-Reisner环的定义,设k是作为系数的交换环,给定任何一个顶点集为{v_1,…,v...
評分Stanley-Reisner环(又称为面环(face ring))把代数拓扑中单纯复形与多项式的单项商环联系起来,可以说是一张通向组合交换代数的入场券,下面就来介绍一下关于它的基本内容。 先看Stanley-Reisner环的定义,设k是作为系数的交换环,给定任何一个顶点集为{v_1,…,v...
Cohen-Macaulay Rings pdf epub mobi txt 電子書 下載 2024