General polynomials over division algebras and left eigenvalues

Ela General Polynomials over Division Algebras and Left Eigenvalues

In this paper, we present an isomorphism between the ring of general polynomials over a division algebra D with center F and the group ring of the free monoid with [D : F ] variables over D. Using this isomorphism, we define the characteristic polynomial of any matrix over any division algebra, i.e., a general polynomial with one variable over the algebra whose roots are precisely the left eige...

General polynomials over division algebras and left eigenvalues

In this paper, we present an isomorphism between the ring of general polynomials over a division algebra D with center F and the group ring of the free monoid with [D : F ] variables over D. Using this isomorphism, we define the characteristic polynomial of any matrix over any division algebra, i.e., a general polynomial with one variable over the algebra whose roots are precisely the left eige...

Triangulaizability of Algebras Over Division Rings

triangulaizability of algebras over division rings

Wedderburn Polynomials over Division Rings

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...