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February 25, 2026Turkish Journal of Mathematics and Computer Science0 citationsOpen Access

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

DDDung Banh Duc

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.

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Cite This Study

Dung Banh Duc (2026) studied this question.

synapsesocial.com/papers/699e918df5123be5ed04f17ehttps://doi.org/10.47000/tjmcs.1689839
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