THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS
Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 193-199

Voir la notice de l'article provenant de la source Cambridge University Press

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)).
DOI : 10.1017/S001708951100053X
Mots-clés : 16Z05, 16P10
HORVÁTH, GÁBOR. THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 193-199. doi: 10.1017/S001708951100053X
@article{10_1017_S001708951100053X,
     author = {HORV\'ATH, G\'ABOR},
     title = {THE {COMPLEXITY} {OF} {THE} {EQUIVALENCE} {PROBLEM} {OVER} {FINITE} {RINGS}},
     journal = {Glasgow mathematical journal},
     pages = {193--199},
     year = {2012},
     volume = {54},
     number = {1},
     doi = {10.1017/S001708951100053X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951100053X/}
}
TY  - JOUR
AU  - HORVÁTH, GÁBOR
TI  - THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS
JO  - Glasgow mathematical journal
PY  - 2012
SP  - 193
EP  - 199
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951100053X/
DO  - 10.1017/S001708951100053X
ID  - 10_1017_S001708951100053X
ER  - 
%0 Journal Article
%A HORVÁTH, GÁBOR
%T THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS
%J Glasgow mathematical journal
%D 2012
%P 193-199
%V 54
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951100053X/
%R 10.1017/S001708951100053X
%F 10_1017_S001708951100053X

[1] 1.Burris, S. and Lawrence, J., Term rewrite rules for finite fields, Int. J. Algebr. Comput. 1 (1991), 353–369. Google Scholar | DOI

[2] 2.Burris, S. and Lawrence, J., The equivalence problem for finite rings, J. Symb. Comp. 15 (1993), 67–71. Google Scholar | DOI

[3] 3.Hazewinkel, M., Gubareni, N. and Kirichenko, V. V., Algebras, rings and modules, vol. 1 (Springer, New York, 2004). Google Scholar

[4] 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. Google Scholar | DOI

[5] 5.Hunt, H. and Stearns, R., The complexity for equivalence for commutative rings, J. Symb. Comp. 10 (1990), 411–436. Google Scholar | DOI

[6] 6.Lawrence, J. and Willard, R., The complexity of solving polynomial equations over finite rings (manuscript, 1997). Google Scholar

[7] 7.MacDonald, B. R., Finite rings with identity (M. Dekker, New York, 1974). Google Scholar

[8] 8.Raghavendran, R., Finite associative rings, Comp. Math. 21 (2) (1969), 195–229. Google Scholar

[9] 9.Szabó, Cs. and Vértesi, V., The equivalence problem over finite rings, Internat. J. Algebra Comput. 21 (3) (2011), 449–457. Google Scholar

[10] 10.Wilson, R. S., On the structure of finite rings, Comp. Math. 26 (1) (1973), 79–93. Google Scholar

Cité par Sources :