2011/10/10 by Chapman, Adam
#11R52 #12E15 #16S10 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1110.2021
In this paper, we present an isomorphism between the ring of general polynomials over a division ring of degree p over its center F and the group ring of the free monoid with p2 variables. Using this isomorphism, we define the characteristic polynomial of a matrix over any division algebra, i.e. a general polynomial with one variable over the algebra whose roots are precisely the left eigenvalues. Plus, we show how the left eigenvalues of a 4 × 4 matrices over any division algebra can be found by solving a general polynomial equation of degree 6 over that algebra.