Reflexive properties of rings determined by idempotents

Authors

  • Liang Zhao School of Microelectronics and Date Science, Anhui University of Technology, Maanshan, China
  • Xiaojie Li School of Microelectronics and Date Science, Anhui University of Technology, Maanshan, China

DOI:

https://doi.org/10.3842/umzh.v77i6.8537

Keywords:

right e-reflexive ring; right e-reduced ring; right e-reversible ring

Abstract

UDC 512.5

We study the reflexive properties of rings determined by idempotents in a more general setting. А new concept named right $e$-reflexive rings is defined and studied. This is a generalization of reflexive rings and right $e$-reversible rings. Some necessary examples and counterexamples are given. Furthermore, we consider the restriction of the right $e$-reflexivity to nilpotent elements, which strictly contains the classes of reflexive rings and right $e$-reflexive rings.  Some well-known results on reflexive rings are unified and extended.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 6, 2025.

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Published

01.08.2025

Issue

Vol. 77 No. 6 (2025)

Section

Research articles

License

Copyright (c) 2025 Liang Zhao, Xiaojie Li

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Zhao, Liang, and Xiaojie Li. “Reflexive Properties of Rings Determined by Idempotents”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 6, Aug. 2025, pp. 447–448, https://doi.org/10.3842/umzh.v77i6.8537.