Bibliographic Information: Azarang, A. (2024). Maximal Subrings of Division Rings. arXiv preprint arXiv:2410.09051v1.
Research Objective: This paper aims to characterize the structure of maximal subrings in division rings and explore the conditions under which such subrings exist.
Methodology: The author employs a theoretical and proof-based approach, drawing upon concepts from ring theory, field extensions, and valuation theory. The paper leverages existing results on maximal subrings in fields and extends them to the non-commutative setting of division rings.
Key Findings:
Main Conclusions: The research provides a comprehensive analysis of maximal subrings in division rings, highlighting their structural characteristics and the conditions governing their existence. The findings contribute to a deeper understanding of the algebraic structure of division rings and their subrings.
Significance: This work enhances the understanding of non-commutative ring theory, particularly in the context of division rings. The results have implications for the study of field extensions, valuation theory, and the structure of non-commutative rings in general.
Limitations and Future Research: The paper primarily focuses on the theoretical aspects of maximal subrings in division rings. Further research could explore specific examples and applications of these findings in other areas of mathematics or related fields. Additionally, investigating the properties of maximal subrings in more specialized types of division rings could yield further insights.
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by Alborz Azara... at arxiv.org 10-15-2024
https://arxiv.org/pdf/2410.09051.pdfDeeper Inquiries