Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-29T00:25:12.777Z Has data issue: false hasContentIssue false
  • English
  • Français

THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS

Published online by Cambridge University Press:  09 December 2011

GÁBOR HORVÁTH
GÁBOR HORVÁTH*
Affiliation:
Institute of Mathematics, University of Debrecen, Pf. 12, Debrecen, 4010, Hungary e-mail: ghorvath@science.unideb.hu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the complexity of the equivalence problem over a finite ring when the input polynomials are written as sum of monomials. We prove that for a finite ring if the factor by the Jacobson radical can be lifted in the centre, then this problem can be solved in polynomial time. This result provides a step in proving a dichotomy conjecture of Lawrence and Willard (J. Lawrence and R. Willard, The complexity of solving polynomial equations over finite rings (manuscript, 1997)).

Keywords

16Z0516P10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 193 - 199
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Burris, S. and Lawrence, J., Term rewrite rules for finite fields, Int. J. Algebr. Comput. 1 (1991), 353–369.CrossRefGoogle Scholar
2.Burris, S. and Lawrence, J., The equivalence problem for finite rings, J. Symb. Comp. 15 (1993), 67–71.CrossRefGoogle Scholar
3.Hazewinkel, M., Gubareni, N. and Kirichenko, V. V., Algebras, rings and modules, vol. 1 (Springer, New York, 2004).Google Scholar
4.Horváth, G., Lawrence, J., Mérai, L. and Szabó, Cs., The complexity of the equivalence problem for non-solvable groups, B. Lond. Math. Soc. 39 (3) (2007), 433–438.CrossRefGoogle Scholar
5.Hunt, H. and Stearns, R., The complexity for equivalence for commutative rings, J. Symb. Comp. 10 (1990), 411–436.CrossRefGoogle Scholar
6.Lawrence, J. and Willard, R., The complexity of solving polynomial equations over finite rings (manuscript, 1997).Google Scholar
7.MacDonald, B. R., Finite rings with identity (M. Dekker, New York, 1974).Google Scholar
8.Raghavendran, R., Finite associative rings, Comp. Math. 21 (2) (1969), 195–229.Google Scholar
9.Szabó, Cs. and Vértesi, V., The equivalence problem over finite rings, Internat. J. Algebra Comput. 21 (3) (2011), 449–457.Google Scholar
10.Wilson, R. S., On the structure of finite rings, Comp. Math. 26 (1) (1973), 79–93.Google Scholar