Tripotent elements in quaternion rings over ℤ_p

[1] N. C. Ankeny, Sum of Three Squares, Proc. Amer. Math. Soc., 8 (2) (1957), 316–319.10.1090/S0002-9939-1957-0085275-8 Search in Google Scholar

[2] M. Aristidou and A. Demetre, A Note on Quaternion Rings over ℤ_p, Int. J. Algebra, 3 (15) (2009), 725–728. Search in Google Scholar

[3] M. Aristidou and A. Demetre, Idempotent Elements in Quaternion Rings over ℤ_p, Int. J. Algebra, 6 (5) (2012), 249–254. Search in Google Scholar

[4] P. Damianou, Commutative Rings (in Greek), Proceedings of the 9^th Cyprus Conference of Mathematics Education and Science, Cyprus, 2007, 165–166. Search in Google Scholar

[5] I. N. Herstein, Topics in Algebra, 2^nd ed., Wiley, NY, 1975. Search in Google Scholar

[6] C. J. Miguel and R. Serodio, On the Structure of Quaternion Rings over ℤ_p, Int. J. Algebra, 5 (27) (2011), 1313–1325. Search in Google Scholar

[7] D. Mosic, Characterizations of k-potent Elements in Rings, Ann. Mat. Pura Appl., 194 (4) (2015), 1157–116810.1007/s10231-014-0415-5 Search in Google Scholar

[8] R. S. Pierce, Associative Algebras, Springer, NY, 1982.10.1007/978-1-4757-0163-0 Search in Google Scholar

[9] R. Remmert, H. D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch and A.Prestel, Numbers, Springer, NY, 1991. Search in Google Scholar

[10] R. D. Schafer, An Introduction to Nonassociative Algebrass, Academic Press, NY, 1966. Search in Google Scholar

[11] J. P. Serre, A Course in Arithmetic, Springer, NY, 1973.10.1007/978-1-4684-9884-4 Search in Google Scholar

[12] G. Trenkler and O. M. Baksalary, On k-potent Matrices, Electron. J. Linear Algebra, 26 (2013), 446–470. Search in Google Scholar

[13] Y. Wu, k-Potent Matrices - Construction and Applications in Digital Image Encryption, Recent Advances in Applied Mathematics, Proceedings of the 2010 American Conference on Applied Mathematics, USA, 2010, 455–460. Search in Google Scholar

[14] Z. Ying, T. Kosan and Y. Zhou, Rings in Which Every Element is a Sum of Two Tripotents, Canad. Math. Bull., 59 (3) (2016), 661–672.10.4153/CMB-2016-009-0 Search in Google Scholar