TY - JOUR
T1 - The images of noncommutative polynomials evaluated on the quaternion algebra
AU - Malev, Sergey
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/5
Y1 - 2021/5
N2 - Let p be a multilinear polynomial in several noncommuting variables with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set Mn(K) of n by n matrices is a vector space. In this paper, we settle the analogous conjecture for a quaternion algebra.
AB - Let p be a multilinear polynomial in several noncommuting variables with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set Mn(K) of n by n matrices is a vector space. In this paper, we settle the analogous conjecture for a quaternion algebra.
KW - Kaplansky conjecture
KW - Noncommutative polynomials
KW - quaternion algebra
UR - http://www.scopus.com/inward/record.url?scp=85082186970&partnerID=8YFLogxK
U2 - 10.1142/S0219498821500742
DO - 10.1142/S0219498821500742
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AN - SCOPUS:85082186970
SN - 0219-4988
VL - 20
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 5
M1 - 2150074
ER -