4 papers
Factorization of central polynomials over division algebras
A. G. Goutor, S. V. Tikhonov
The factorization problem is a classical topic in the theory of polynomial rings. In this paper, we obtain an irreducibility criterion for central polynomials over division algebra…
Polynomials over division rings
Alina G. Goutor, Sergey V. Tikhonov
We consider properties of polynomials with coefficients in division rings. A theorem on the decomposition of a polynomial with coefficients in an arbitrary division ring is obtaine…
Existence of polynomials with given roots over non-commutative rings
Alina G. Goutor
The paper studies the question of existence of polynomials with given roots over associative non-commutative rings with identity. It is shown that in the case of an associative div…
Roots of polynomials over division rings
Alina G. Goutor, Sergey V. Tikhonov
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials