PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
February 25, 2026Turkish Journal of Mathematics and Computer Science0 citationsOpen Access

On ADS^- (pre) covers and ADS^- (pre) envelopes modules

DDDung Banh DucHo Chi Minh City University of Technology and Education

Key Points

  • The study aims to determine conditions under which modules possess ADS$^{ullet}$-preenvelopes and covers.
  • Examined the properties of ADS$^{ullet}$ modules over a ring R.
  • Proved equivalencies relating projective modules to the existence of ADS$^{ullet}$-preenvelopes and covers.
  • Introduced a generalization of ADS$^{ullet}$ modules focusing on their behavior under automorphisms.
  • Demonstrated that every ADS$^{ullet}$ module over a ring is projective if it has ADS$^{ullet}$-preenvelopes.
  • Established the necessity of ADS$^{ullet}$-(pre)covers for the modular properties in the context studied.
  • Provided insights into the categorization and properties of modules through automorphisms.

Abstract

The objective of this paper is to study the question of when modules have ADS^-preenvelopes and covers. It is proved that every ADS^ module over a ring R is projective if and only if every right R-module has an ADS^- (pre) envelope (an ADS^- (pre) cover). We also introduce a generalization of ADS^ modules in terms of their invariance under certain automorphisms of their envelopes.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Dung Banh Duc (2026) studied this question.

synapsesocial.com/papers/699e918df5123be5ed04f17ehttps://doi.org/10.47000/tjmcs.1689839
Ask AI
Helpful
Bookmark
Share
View Full Paper