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Krull-Remak-Schmidt decompositions in Hom-finite additive categories

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Standard

Krull-Remak-Schmidt decompositions in Hom-finite additive categories. / Shah, Amit.
I: Expositiones Mathematicae, Bind 41, Nr. 1, 03.2023, s. 220-237.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Harvard

Shah, A 2023, 'Krull-Remak-Schmidt decompositions in Hom-finite additive categories', Expositiones Mathematicae, bind 41, nr. 1, s. 220-237. https://doi.org/10.1016/j.exmath.2022.12.003

APA

Shah, A. (2023). Krull-Remak-Schmidt decompositions in Hom-finite additive categories. Expositiones Mathematicae, 41(1), 220-237. https://doi.org/10.1016/j.exmath.2022.12.003

CBE

Shah A. 2023. Krull-Remak-Schmidt decompositions in Hom-finite additive categories. Expositiones Mathematicae. 41(1):220-237. https://doi.org/10.1016/j.exmath.2022.12.003

MLA

Shah, Amit. "Krull-Remak-Schmidt decompositions in Hom-finite additive categories". Expositiones Mathematicae. 2023, 41(1). 220-237. https://doi.org/10.1016/j.exmath.2022.12.003

Vancouver

Shah A. Krull-Remak-Schmidt decompositions in Hom-finite additive categories. Expositiones Mathematicae. 2023 mar.;41(1):220-237. doi: 10.1016/j.exmath.2022.12.003

Author

Shah, Amit. / Krull-Remak-Schmidt decompositions in Hom-finite additive categories. I: Expositiones Mathematicae. 2023 ; Bind 41, Nr. 1. s. 220-237.

Bibtex

@article{198271e26e78407781bdef40fec43af3,
title = "Krull-Remak-Schmidt decompositions in Hom-finite additive categories",
abstract = "An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is known as a Krull-Schmidt category. A Hom-finite category is an additive category A for which there is a commutative unital ring k, such that each Hom-set in A is a finite length k-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring.",
keywords = "Additive category, Hom-finite category, Idempotent, Krull-Remak-Schmidt decomposition, Krull-Schmidt category, Split idempotents",
author = "Amit Shah",
year = "2023",
month = mar,
doi = "10.1016/j.exmath.2022.12.003",
language = "English",
volume = "41",
pages = "220--237",
journal = "Expositiones Mathematicae",
issn = "0723-0869",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Krull-Remak-Schmidt decompositions in Hom-finite additive categories

AU - Shah, Amit

PY - 2023/3

Y1 - 2023/3

N2 - An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is known as a Krull-Schmidt category. A Hom-finite category is an additive category A for which there is a commutative unital ring k, such that each Hom-set in A is a finite length k-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring.

AB - An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is known as a Krull-Schmidt category. A Hom-finite category is an additive category A for which there is a commutative unital ring k, such that each Hom-set in A is a finite length k-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring.

KW - Additive category

KW - Hom-finite category

KW - Idempotent

KW - Krull-Remak-Schmidt decomposition

KW - Krull-Schmidt category

KW - Split idempotents

U2 - 10.1016/j.exmath.2022.12.003

DO - 10.1016/j.exmath.2022.12.003

M3 - Journal article

VL - 41

SP - 220

EP - 237

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

SN - 0723-0869

IS - 1

ER -