Direct sum decomposition and weak Krull-Schmidt Theorems

Name: Direct sum decomposition and weak Krull-Schmidt Theorems
Brand: LAP Lambert Academic Publishing
SKU: 9783846598740
Price: 62.04 EUR
Availability: InStock

A survey on weak Krull-Schmidt Theorems

Автор: Marco Perone

Език:

Корици: С меки корици

Издател: LAP Lambert Academic Publishing

Наличност: Външен склад

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62.04 € 121.34 лв

In this book we discuss the behaviour of direct sum decomposition in additive categories and in part...

Информация за книгата

Автор

Marco Perone

Език

Английски език

Корици

Книга - С меки корици

Издадена

2011

страници

172

EAN

9783846598740

Enbook ID

07046708

Издател

LAP Lambert Academic Publishing

Теглоt

267

Размери

150 x 220 x 10

Пълно описание

In this book we discuss the behaviour of direct sum decomposition in additive categories and in particular in categories of modules. In the first part, we investigate the ring theoretical properties that play a main role in the theory of factorization in additive categories, like the exchange property, semilocality and Goldie dimension. We stress the importance of the latter and we investigate with care the infinite case of the dual Goldie dimension of rings. In the rest of the book, we use a more categorical approach, studying the behaviour of direct sum decomposition in additive categories. We study classes of categories where the direct sum decomposition behaves regularly, underlining the role played by semilocal endomorphism rings. We analyze the peculiar behaviour of direct sum decomposition in some categories of modules, where the uniqueness of the decomposition is obtained up to two permutations, and we notice how this phenomenon is due to the presence of endomorphism rings of type two. In the last chapter we investigate what happens when we pass from finite direct sum of indecomposable objects to infinite direct sums both at a categorical and a monoid theoretical level.

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Direct sum decomposition and weak Krull-Schmidt Theorems

A survey on weak Krull-Schmidt Theorems

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Пълно описание

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