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PreprintarXiv licencearXiv

On strongly m-Δ-clean ring

  • Saikat Das
  • Sukhendu Kar
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Abstract

Motivated by the recent study of strongly Δ-clean rings, we introduce and study strongly m-Δ-clean rings. We establish their fundamental properties and characterize strongly m-Δ-clean rings via lifting m-potent elements modulo Δ(R). We prove that every m-Δ-clean ring is clean and that the factor ring of a strongly m-Δ-clean ring modulo its Jacobson radical is reduced. Finally, we investigate corner rings, Morita context rings, and the relationships of these rings with Δ-clean, local, semipotent, and strongly m-nil clean rings.

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Cite

BibTeXRIS
BibTeX
@misc{das2026strongly,
  title = {{On strongly $m$-$Δ$-clean ring}},
  author = {Saikat Das and Sukhendu Kar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.01678},
  eprint = {2609.01678},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01678},
}
RIS
TY  - UNPB
TI  - On strongly m-Δ-clean ring
AU  - Saikat Das
AU  - Sukhendu Kar
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01678
UR  - https://arxiv.org/abs/2609.01678
AB  - Motivated by the recent study of strongly Δ-clean rings, we introduce and study strongly m-Δ-clean rings. We establish their fundamental properties and characterize strongly m-Δ-clean rings via lifting m-potent elements modulo Δ(R). We prove that every m-Δ-clean ring is clean and that the factor ring of a strongly m-Δ-clean ring modulo its Jacobson radical is reduced. Finally, we investigate corner rings, Morita context rings, and the relationships of these rings with Δ-clean, local, semipotent, and strongly m-nil clean rings.
ER  -