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NONCOMMUTATIVE POLYNOMIAL MAPS

ANDRÉ LEROY

Université d'Artois, Faculté Jean Perrin, Rue Jean Souvraz 62 307 Lens, France

https://doi.org/10.1142/S0219498812500764Cited by:24 (Source: Crossref)

Abstract

Polynomial maps attached to polynomials of an Ore extension are naturally defined. In this setting we show the importance of pseudo-linear transformations and give some applications. In particular, factorizations of polynomials in an Ore extension over a finite field 𝔽_q[t;θ], where θ is the Frobenius automorphism, are translated into factorizations in the usual polynomial ring 𝔽_q[x].

Keywords:

References

D. Boucher, W. Geiselmann and F. Ulmer, Appl. Algebra Eng. Comm. Comput. 18, 379 (2007). Crossref, Web of Science, Google Scholar
D. Boucher and F. Ulmer, J. Symbolic Comput. 44, 1644 (2009). Crossref, Web of Science, Google Scholar
M. Christofeul, Ph.D. Thesis, Université d'Artois, in preparation . Google Scholar
P. M. Cohn , Skew Fields: Theory of General Division Rings , Encyclopedia of Mathematics and its Applications 57 ( Cambridge University Press , Cambridge , 1995 ) . Crossref, Google Scholar
J. Delenclos and A. Leroy, J. Algebra Appl. 6, 815 (2007). Link, Web of Science, Google Scholar
D. E. Haile and L. H. Rowen, Algebra Colloq. 2, 145 (1995). Google Scholar
N. Jacobson, Ann. of Math. 38, 484 (1937). Crossref, Google Scholar
N. Jacobson , Lectures in Abstract Algebra 3 ( Van Nostrand , 1964 ) . Crossref, Google Scholar
T. Y. Lam , A First Course in Noncommutative Rings , Graduate Texts in Mathematics 131 ( Springer-Verlag , Berlin , 1991 ) . Crossref, Google Scholar
T. Y. Lam and A. Leroy, J. Algebra 119, 308 (1988). Crossref, Web of Science, Google Scholar
T. Y. Lam and A. Leroy, Perspectives in Ring Theory, eds. F. van Oystaeyen and L. Le Bruyn (Kluwer Academic Publishers, Dordrecht, 1988) pp. 153–203. Crossref, Google Scholar
T. Y. Lam and A. Leroy, Trans. Amer. Math. Soc. 345, 595 (1994). Web of Science, Google Scholar
T. Y. Lam and A. Leroy, J. Pure Appl. Algebra 186, 43 (2004). Crossref, Web of Science, Google Scholar
T. Y. Lam, A. Leroy and A. Ozturk, Noncommutative Rings, Group Rings, Diagram Algebras and their Applications, Contemporary Mathematics 456 (American Mathematical Society, Providence, RI, 2008) pp. 73–98. Crossref, Google Scholar
A. Leroy, Bull. Belg. Math. Soc. 2, 321 (1995). Web of Science, Google Scholar
A. Leroy and A. Ozturk, Comm. Algebra 32(5), 1763 (2004). Crossref, Web of Science, Google Scholar
H. Bourlès and B. Marinescu, Systems Control Lett. 58, 248 (2009). Web of Science, Google Scholar
B. Marinescu and H. Bourlès , Linear Time-Varying Systems Algebraic-Analytic Approach , Lectures Notes in Control and Informations Sciences 410 ( Springer-Verlag , 2011 ) . Google Scholar
O. Ore, Ann. Math. 34, 480 (1933). Crossref, Google Scholar