Ideals, radicals, and structure of additive categories

Ross Street

doi:10.1007/BF00877633

Ideals, radicals, and structure of additive categories

Ross Street^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid.

Original language	English
Pages (from-to)	139-149
Number of pages	11
Journal	Applied Categorical Structures
Volume	3
Issue number	2
DOIs	https://doi.org/10.1007/BF00877633
Publication status	Published - Jun 1995

Keywords

Additive category
artinian
density arguments
Jacobson
Mathematics subject classifications (1991): 18E05, 16A20, 16A40
radical
semiprimitive ring
simple

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10.1007/BF00877633

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abstract = "Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid.",

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AB - Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid.

KW - Additive category

KW - artinian

KW - density arguments

KW - Jacobson

KW - Mathematics subject classifications (1991): 18E05, 16A20, 16A40

KW - radical

KW - semiprimitive ring

KW - simple

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DO - 10.1007/BF00877633

M3 - Article

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SP - 139

EP - 149

JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 2

ER -

Ideals, radicals, and structure of additive categories

Abstract

Keywords

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