Relatively divisible and relatively flat objects in exact categories: applications

Septimiu Crivei; Derya Keskin Tütüncü

doi:10.1007/s00200-021-00487-7

Relatively divisible and relatively flat objects in exact categories: applications

Septimiu Crivei
, Derya Keskin Tütüncü

Division of Algebra and Number Theory

Babes-Bolyai University

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

Abstract

For a Quillen exact category C endowed with two exact structures D and E such that E⊆ D, an object X of C is called E-divisible (respectively E-flat) if every short exact sequence from D starting (respectively ending) with X belongs to E. We continue our study of relatively divisible and relatively flat objects in Quillen exact categories with applications to finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.

Original language	English
Pages (from-to)	365-384
Number of pages	20
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s00200-021-00487-7
Publication status	Published - Jun 2021

Keywords

Cotorsion pair
Divisible object
Exact category
Finitely accessible additive category
Flat object
Jacobson radical
Module category
Pure short exact sequence
Simple module

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10.1007/s00200-021-00487-7

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KW - Cotorsion pair

KW - Divisible object

KW - Exact category

KW - Finitely accessible additive category

KW - Flat object

KW - Jacobson radical

KW - Module category

KW - Pure short exact sequence

KW - Simple module

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IS - 3

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Relatively divisible and relatively flat objects in exact categories: applications

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Keywords

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