Krull-Schmidt categories and projective covers

By Henning Krause. 2014

187 citations recorded by the source corpus.

Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1d119022fc0f98b01afa958d43c1af228c0b97ab

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Julian Kulshammer
2. Gustavo Jasso

In Geometry and Topology

1. Julian Kulshammer
2. Gustavo Jasso
3. Lidia Angeleri Hugel
4. Thomas Brustle

In Mathematical Physics

1. Julian Kulshammer
2. Gustavo Jasso
3. Lidia Angeleri Hugel

Citations in the corpus

• Higher Nakayama algebras I: Construction (2016, background): “ every pair of objects x;y2A the vector space of morphisms A(x;y) is nite dimensional; note that this property implies that the Krull{ Schmidt theorem holds in projA, see for example Corollary 4.4 in [Kra15]. Let A be a locally nite dimensional category. In order to simplify the exposition we make t”