## Revista Matemática Iberoamericana

### Nonassociative Algebras: Some Applications

#### Abstract

Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.

#### Article information

Source
Rev. Mat. Iberoamericana Volume 19, Number 2 (2003), 385-392.

Dates
First available in Project Euclid: 8 September 2003

https://projecteuclid.org/euclid.rmi/1063050159

Mathematical Reviews number (MathSciNet)
MR2023191

Zentralblatt MATH identifier
1071.17019

#### Citation

González, Santos; Martínez, Consuelo. Nonassociative Algebras: Some Applications. Rev. Mat. Iberoamericana 19 (2003), no. 2, 385--392. https://projecteuclid.org/euclid.rmi/1063050159

#### References

• Bartholdi, L. and Grigorchuck, R. I.: Lie methods in growth of groups of finite width. In Computational and geometric aspects of modern algebra (Edinburgh, 1998), 1-27. London Math. Soc. Lecture Notes Ser. 275. Cambridge Univ. Press, 2000.
• Elduque, A. and Myung, H. C.: Mutations of Alternative Algebras. Mathematics and its Applications 278. Kluwer, Dordrecht, 1994.
• Elduque, A. and Myung, H. C.: The reductive pair $(B_4,B_3)$ and affine connections on $S^15$. J. Algebra 227 (2000), no. 2, 504-531.
• González, S., Markov, V. T., Martínez, C., Nechaev, A. A. and Rúa, I. F.: Nonassociative Galois rings. Discrete Math. Appl. 12 (2002), 591-606.
• Grigorchuk, R. I.: On the Burnside problem for periodic groups. Funct. Anal. Appl. 14 (1980), 53-54.
• Hopkins, N. C.: Quadratic differential equations in graded algebras. In Nonassociative Algebra and its Applications (S. González ed.), 179-182. Math. Appl. 303, Kluwer Acad. Publ., 1994.
• Janusz, G.J.: Separable algebras over commutative rings. Trans. Amer. Math. Soc. 122 (1966), 461-478.
• Krull, W.: Algebraische Theory der Ringe II. Math. Ann. 91 (1924), 1-46.
• Kuzmin, A. S. and Nechaev, A. S.: Linear recurring sequences over Galois Rings. Algebra and Logic 34 (1995), no. 2, 87-100.
• Markus, L.: Quadratic differential equations and nonassociative algebras. Annals of Math. Stud. 45 (1960), 185-213.
• Martínez, C. and Zelmanov, E.: Jordan algebras of Gelfand-Kirillov dimension 1. J. Algebra 180 (1996), no. 1, 211-238.
• Martínez, C. and Zelmanov, E.: Nil Algebras and Unipotent Groups of Finite Width. Adv. Math. 147 (1999), 328-344.
• Nechaev, A. A.: Kerdock's code in cyclic form. Discrete Math. Appl. 1 (1989), no. 4, 365-384.
• Raghavendran, R.: Finite associative rings. Compositio Math. 21 (1969), no. 2, 195-219.
• Reed, M. L.: Algebraic structures of genetic inheritance. Bull. Amer. Math. Soc. 34 (1997), 107-130.
• Small, L. W., Stafford, J. T. and Warfield Jr., R. B.: Affine algebras of Gelfand-Kirillov dimension 1 are PI. Math. Proc. Cambridge Philos. Soc. 97 (1985), 407-414.
• Zhevlakov, K. A., Slinko, A. M., Shestakov, I. P. and Shirshov, A. I.: Rings that are nearly associative. Academic Press, New York, 1982.