Polyadic Rings of p-Adic Integers
Abstract
:1. Introduction
2. -Rings of Integer Numbers from Residue Classes
3. Representations of p-Adic Integers
4. -Rings of p-Adic Integers
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Neurkich, J. Algebraic Number Theory; Springer: Berlin, Germany; New York, NY, USA, 1999. [Google Scholar]
- Samuel, P. Algebraic Theory of Numbers; Hermann: Paris, France, 1972. [Google Scholar]
- Berthelot, P.; Ogus, A. Notes on Crystalline Cohomology; Princeton University Press: Princeton, NJ, USA, 1978. [Google Scholar]
- LeStum, B. Rigid Cohomology; Cambridge University Press: Cambridge, UK, 2007. [Google Scholar]
- Caruso, X. Computations with p-adic numbers. Les Cours du CIRM 2017, 5, 1–75. [Google Scholar] [CrossRef]
- Dragovich, B.; Khrennikov, A.Y.; Kozyrev, S.V.; Volovich, I.V.; Zelenov, E.I. p-Adic mathematical physics: The first 30 years. P-Adic Num. Ultrametr. Anal. Appl. 2017, 9, 87–121. [Google Scholar] [CrossRef]
- Vladimirov, V.S.; Volovich, I.V.; Zelenov, E.I. P-Adic Analysis And Mathematical Physics; World Scientific Publishing: Singapore, 1994; p. 319. [Google Scholar]
- Sarwar, M.; Humaira, H.; Huang, H. Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces. Comment. Math. 2018, 58, 57–78. [Google Scholar] [CrossRef]
- Zada, M.B.; Sarwar, M.; Tunc, C. Fixed point theorems in b-metric spaces and their applications to non-linear fractional differential and integral equations. J. Fixed Point Theor. Appl. 2018, 20, 19. [Google Scholar] [CrossRef]
- Koblitz, N. p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, 2nd ed.; Springer: New York, NY, USA, 1996; p. 150. [Google Scholar]
- Robert, A.M. A Course in p-Adic Analysis; Springer: New York, NY, USA, 2000. [Google Scholar] [CrossRef]
- Schikhof, W.H. Ultrametric Calculus; Cambridge University Press: Cambridge, UK, 1984. [Google Scholar]
- Duplij, S. Polyadic integer numbers and finite (m,n)-fields. P-Adic Num. Ultrametr. Anal. Appl. 2017, 9, 257–281. [Google Scholar] [CrossRef] [Green Version]
- Duplij, S. Arity shape of polyadic algebraic structures. J. Math. Phys. Anal. Geom. 2019, 15, 3–56. [Google Scholar] [CrossRef] [Green Version]
- Duplij, S. Polyadic Algebraic Structures; IOP Publishing: Bristol, UK, 2022; p. 461. [Google Scholar] [CrossRef]
- Gouvêa, F.Q. p-Adic Numbers. An introduction, 3rd ed.; Springer: Cham, Switzerland, 2020. [Google Scholar] [CrossRef]
- Xu, K.; Dai, Z.; Dai, Z. The formulas for the coefficients of the sum and product of p-adic integers with applications to Witt vectors. Acta Arith. 2011, 150, 361–384. [Google Scholar] [CrossRef]
- Dörnte, W. Unterschungen über einen verallgemeinerten Gruppenbegriff. Math. Z. 1929, 29, 1–19. [Google Scholar] [CrossRef]
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Duplij, S. Polyadic Rings of p-Adic Integers. Symmetry 2022, 14, 2591. https://doi.org/10.3390/sym14122591
Duplij S. Polyadic Rings of p-Adic Integers. Symmetry. 2022; 14(12):2591. https://doi.org/10.3390/sym14122591
Chicago/Turabian StyleDuplij, Steven. 2022. "Polyadic Rings of p-Adic Integers" Symmetry 14, no. 12: 2591. https://doi.org/10.3390/sym14122591