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PreprintCC BY 4.0arXiv

Formal Matrix Rings with the Involution Property

  • Valeriya Kirova
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Abstract

We study formal matrix rings with the involution property, that is, rings in which every element can be represented as the sum of an invertible element and an involution. After recalling the construction of formal matrix rings via Morita contexts, we describe involutions in triangular formal matrix rings and establish a criterion for upper triangular rings of order two. We then prove that a formal matrix ring of arbitrary finite order has the involution property whenever all of its diagonal rings have this property. Several examples and counterexamples are included to illustrate the obtained results.

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Cite

BibTeXRIS
BibTeX
@misc{kirova2026formal,
  title = {{Formal Matrix Rings with the Involution Property}},
  author = {Valeriya Kirova},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04709},
  eprint = {2610.04709},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04709},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Formal Matrix Rings with the Involution Property
AU  - Valeriya Kirova
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.04709
UR  - https://arxiv.org/abs/2610.04709
AB  - We study formal matrix rings with the involution property, that is, rings in which every element can be represented as the sum of an invertible element and an involution. After recalling the construction of formal matrix rings via Morita contexts, we describe involutions in triangular formal matrix rings and establish a criterion for upper triangular rings of order two. We then prove that a formal matrix ring of arbitrary finite order has the involution property whenever all of its diagonal rings have this property. Several examples and counterexamples are included to illustrate the obtained results.
ER  -