Finite dimensional factor algebras of F_{2}[*X*_{1}, …, *X*_{n}] and their fixed point subalgebras

ABSTRACT

Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field F2 (with respect to all F2-algebra automorphisms) are fully described.

Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field F2 (with respect to all F2-algebra automorphisms) are fully described.

Cite this paper

nullKureš, M. (2012) Finite dimensional factor algebras of F_{2}[*X*_{1}, …, *X*_{n}] and their fixed point subalgebras. *Open Journal of Applied Sciences*, **2**, 212-214. doi: 10.4236/ojapps.2012.24B048.

nullKureš, M. (2012) Finite dimensional factor algebras of F

References

[1] G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Kluwer Academic Publishers 2002.

[2] B. Fine, “Classification of finite rings of order p2,” Mathematics Magazine 66, No. 4, 1993, pp. 248–252.

[3] J. Hrdina, M. Kure? and P. Va?ík, “A note on tame polynomial automorphisms and the security of TTM cryptosystem,” Applied and Computational Mathematics 9, No. 2, 2010, pp. 226–233.

[4] M. Kure? and W. M. Mikulski, “Natural operators lifting vector fields to bundles of Weil contact elements,” Czechoslovak Mathematical Journal 54 (129), 2004, pp. 855–867.

[5] M. Kure? and W. M. Mikulski, “Natural operators lifting 1-forms to bundles of Weil contact elements,” Bulletin of the Irish Mathematical Society 49, 2002, pp.23–41.

[6] M. Kure? and D. Sehnal, “The order of algebras with nontrivial fixed point subalgebras,” Lobachevskii Journal of Mathematics 25, 2007, pp. 187–198.

[7] M. Kure?, “The composition of polynomials by the substitution principle,” Journal of Discrete Mathematical Sciences & Cryptography 13, No. 6, 2010, pp. 543–552.

[8] M. Kure?, “Fixed point subalgebras of Weil algebras: from geometric to algebraic questions,” in Complex and Differential Geometry, Springer Proceedings of Mathematics, 2011, pp. 183–192.

[1] G. Bini and F. Flamini, Finite Commutative Rings and Their Applications, Kluwer Academic Publishers 2002.

[2] B. Fine, “Classification of finite rings of order p2,” Mathematics Magazine 66, No. 4, 1993, pp. 248–252.

[3] J. Hrdina, M. Kure? and P. Va?ík, “A note on tame polynomial automorphisms and the security of TTM cryptosystem,” Applied and Computational Mathematics 9, No. 2, 2010, pp. 226–233.

[4] M. Kure? and W. M. Mikulski, “Natural operators lifting vector fields to bundles of Weil contact elements,” Czechoslovak Mathematical Journal 54 (129), 2004, pp. 855–867.

[5] M. Kure? and W. M. Mikulski, “Natural operators lifting 1-forms to bundles of Weil contact elements,” Bulletin of the Irish Mathematical Society 49, 2002, pp.23–41.

[6] M. Kure? and D. Sehnal, “The order of algebras with nontrivial fixed point subalgebras,” Lobachevskii Journal of Mathematics 25, 2007, pp. 187–198.

[7] M. Kure?, “The composition of polynomials by the substitution principle,” Journal of Discrete Mathematical Sciences & Cryptography 13, No. 6, 2010, pp. 543–552.

[8] M. Kure?, “Fixed point subalgebras of Weil algebras: from geometric to algebraic questions,” in Complex and Differential Geometry, Springer Proceedings of Mathematics, 2011, pp. 183–192.