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

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.