Relatively divisible and relatively flat objects in exact categories: applications

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Crivei S., KESKİN TÜTÜNCÜ D.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.32, no.3, pp.365-384, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s00200-021-00487-7
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.365-384
  • Keywords: Exact category, Divisible object, Flat object, Cotorsion pair, Finitely accessible additive category, Module category, Pure short exact sequence, Simple module, Jacobson radical, COHERENT RINGS, MODULES, NEAT, COVERS
  • Hacettepe University Affiliated: Yes

Abstract

For a Quillen exact category C endowed with two exact structures D and E such that E subset of D an object X of C is called E-divisible (respectively E-flat) if every short exact sequence from 7, 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.