Download e-book for iPad: Cohen-Macaulay representations by Graham J. Leuschke

By Graham J. Leuschke

ISBN-10: 0821875817

ISBN-13: 9780821875810

This booklet is a entire remedy of the illustration concept of maximal Cohen-Macaulay (MCM) modules over neighborhood jewelry. This subject is on the intersection of commutative algebra, singularity concept, and representations of teams and algebras. introductory chapters deal with the Krull-Remak-Schmidt Theorem on specialty of direct-sum decompositions and its failure for modules over neighborhood jewelry. Chapters 3-10 research the imperative challenge of classifying the jewelry with merely finitely many indecomposable MCM modules as much as isomorphism, i.e., jewelry of finite CM style. the elemental material--ADE/simple singularities, the double branched disguise, Auslander-Reiten thought, and the Brauer-Thrall conjectures--is lined basically and fully. a lot of the content material hasn't ever ahead of seemed in ebook shape. Examples contain the illustration idea of Artinian pairs and Burban-Drozd's comparable building in measurement , an creation to the McKay correspondence from the viewpoint 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

Show description

Read Online or Download Cohen-Macaulay representations PDF

Similar linear books

New PDF release: The Linear Algebra a Beginning Graduate Student Ought to

Linear algebra is a dwelling, lively department of arithmetic that's relevant to nearly all different components of arithmetic, either natural and utilized, in addition to to machine technology, to the actual, organic, and social sciences, and to engineering. It encompasses an intensive corpus of theoretical effects in addition to a wide and rapidly-growing physique of computational options.

Recent Developments in Quantum Affine Algebras and Related - download pdf or read online

This quantity displays the court cases of the overseas convention on Representations of Affine and Quantum Affine Algebras and Their purposes held at North Carolina kingdom collage (Raleigh). in recent times, the speculation of affine and quantum affine Lie algebras has turn into a big region of mathematical examine with a number of purposes in different components of arithmetic and physics.

Additional resources for Cohen-Macaulay representations

Sample text

15, and similarly +(M ) is a subsemigroup of +(M ) for an R-module M . This forces various structural restrictions on which semigroups can arise as V(R) for a local ring R, or as +(M ) for a finitely generated R-module M . In short, +(M ) must be a finitely generated semigroup. In §1 we detail these restrictions, 13 14 2. SEMIGROUPS OF MODULES and in the rest of the chapter we prove two realization theorems, which show that every finitely generated Krull monoid can be realized in the form +(M ) for a suitable local ring R and MCM R-module M .

29). When the multiplicity is three we have to consider the second condition. One can check, for example, that k[[t3 , t5 ]] satisfies (DR2) but that k[[t3 , t7 ]] does not. 16. 17) that a one-dimensional local ring R has finite CM type if and only if its completion does. The analogous statement fails badly in higher dimension without some additional assumptions; cf. Chapter 10. 15 shows that if a one-dimensional CM local ring has finite CM type, then its completion is reduced; in particular R is an 41 42 4.

Now we have α, β ∈ D such that {1, α, β, αβ} is linearly independent and both α2 and β 2 are in k. 3) §2. 5) B = (α2 + tuβ 2 )P + β 2 (HP H + tHP + uP H), A((t − u)I + H) =HA, 37 A = Q, (t + u)P + HP + P H = 0 . Suppose t = u. 16, that P = 0. (Cf. 14, that ϕ is not an isomorphism. Now suppose t = u and ϕ2 = ϕ. 2, we see that both A and P are in k[H]. 2) painlessly. Equating ϕ and ϕ2 , we see that P = 0 and A = A2 . Since k[H] is local, A = 0 or I. 22. Case. s 4. 17, |k| = 2 and Di /mi = k for each i.

Download PDF sample

Cohen-Macaulay representations by Graham J. Leuschke


by Kevin
4.2

Rated 4.07 of 5 – based on 38 votes