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Let K be a field and σ an automorphism of K of order n. Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial fK[t; σ]. We mainly treat the case that K/F is a cyclic field extension of degree n with Galois group generated by σ.We obtain lower bounds on the dimension of the eigenspace, and compute it in special cases as a quotient algebra. Conditions under which a monic polynomial fF [t] ⊂ K[t; σ] is reducible are obtained in special cases.

eISSN:
1844-0835
Idioma:
Inglés
Calendario de la edición:
Volume Open
Temas de la revista:
Mathematics, General Mathematics