Zero Divisors in Associative Algebras over Infinite Fields
Michael Schweitzer, Steven Finch
Abstract
Let F be an infinite field. We prove that the right zero divisors of a three-dimensional associative F-algebra A must form the union of at most finitely many linear subspaces of A. The proof is elementary and written with students as the intended audience.
Create a lesson
Related papers
Free Novikov-Zinbiel algebra
A. Dauletiyarova, F. Mashurov, B. Sartayev
Very good gradings on structural matrix rings
Patrik Lundström, Johan Öinert, Laura Orozco et al.
Relation graphs of the sedenion algebra
Alexander Guterman, Svetlana Zhilina
On doubly alternative zero divisors in Cayley-Dickson algebras
Svetlana Zhilina
Diameter of the commutativity graph of the real sedenions
Svetlana Zhilina
Functional identities of degree 2 at two-sided zero products on incidence algebras
Hongyu Jia, Zhankui Xiao