By Graham J. Leuschke
This publication is a accomplished remedy of the illustration conception of maximal Cohen-Macaulay (MCM) modules over neighborhood earrings. This subject is on the intersection of commutative algebra, singularity conception, and representations of teams and algebras. introductory chapters deal with the Krull-Remak-Schmidt Theorem on forte of direct-sum decompositions and its failure for modules over neighborhood jewelry. Chapters 3-10 examine the valuable challenge of classifying the jewelry with in basic terms finitely many indecomposable MCM modules as much as isomorphism, i.e., earrings of finite CM style. the elemental material--ADE/simple singularities, the double branched disguise, Auslander-Reiten concept, and the Brauer-Thrall conjectures--is lined in actual fact and fully. a lot of the content material hasn't ever ahead of seemed in ebook shape. Examples comprise the illustration concept of Artinian pairs and Burban-Drozd's similar development in size , an advent to the McKay correspondence from the perspective of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation conception, and a cautious therapy of nonzero attribute. the rest seven chapters current effects on bounded and countable CM sort and at the illustration conception of completely reflexive modules
Read or Download Cohen-Macaulay representations PDF
Best linear books
Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics
This publication is meant as an introductory textual content with reference to Lie teams and algebras and their function in numerous fields of arithmetic and physics. it really is written via and for researchers who're essentially analysts or physicists, no longer algebraists or geometers. no longer that we've got eschewed the algebraic and geo metric advancements.
Dimensional Analysis. Practical Guides in Chemical Engineering
Sensible courses in Chemical Engineering are a cluster of brief texts that every presents a concentrated introductory view on a unmarried topic. the whole library spans the most subject matters within the chemical technique industries that engineering execs require a uncomplicated figuring out of. they're 'pocket courses' that the pro engineer can simply hold with them or entry electronically whereas operating.
Can one research linear algebra completely by way of fixing difficulties? Paul Halmos thinks so, and you'll too when you learn this ebook. The Linear Algebra challenge e-book is a perfect textual content for a direction in linear algebra. It takes the scholar step-by-step from the fundamental axioms of a box during the proposal of vector areas, directly to complex ideas corresponding to internal product areas and normality.
- Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
- Linear Programming: Mathematics, Theory and Algorithms
- Selected Papers of E. B. Dynkin with Commentary (Collected Works)
- Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations (Mathematics and Its Applications)
- Algebraic Projective Geometry (Oxford Classic Texts in the Physical Sciences)
- Electro-Osmosis of Polymer Solutions: Linear and Nonlinear Behavior (Springer Theses)
Extra resources for Cohen-Macaulay representations
Example text
Reflexive) ideal J ∗∗ , where −∗ denotes the dual HomR (−, R). 2) 0 −→ F −→ M −→ J −→ 0 wherein F is a free R-module and J is an ideal of R. The following criterion for a module to be extended is Proposition 3 of [RWW99] (cf. 5)]). 15. Proposition. Let R be a two-dimensional local ring whose m-adic completion R is a normal domain. Let N be a finitely generated torsion-free R-module. Then N is extended from R if and only if cl(N ) is in the image of the natural homomorphism Φ : Cl(R) −→ Cl(R). Proof.
9, we get a local ring R and indecomposable R-modules A, B, C such that A(t) has only the obvious direct-sum decompositions for t 72, but A(73) ∼ = B ⊕ C. We define the splitting number spl(R) of a one-dimensional local ring R by spl(R) = Spec(R) − |Spec(R)| . 9 is s − 1. 12 says that every finitely generated Krull monoid defined by m equations can be realized as +(M ) for some finitely generated module over a one-dimensional local ring (in fact, a domain essentially of finite type over Q) with splitting number m.
The functor (V → W ) (V → B ⊗C W ) from (A → C)-mod to (A → B)-mod is faithful and full. The functor is injective on isomorphism classes and preserves indecomposability. 11. Lemma. For a nilpotent ideal I of B, let E = A+I → BI . I V +IW W The functor (V → W ) → IW , from A-mod to E-mod, is IW surjective on isomorphism classes and reflects indecomposable objects. 12. Proposition. Let A → B be an Artinian pair for which either (dr1) or (dr2) fails. There is a ring C between A and B such that, with D = C/mC, we have either (i) dimk (D) 4, or (ii) D contains elements α and β such that {1, α, β} is linearly independent over k and α2 = αβ = β 2 = 0.