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- Title
THE STRUCTURE OF MATRIX POLYNOMIAL ALGEBRAS.
- Authors
Nguefack, Bertrand
- Abstract
This work formally introduces and starts investigating the structure of matrix polynomial algebra extensions of a coefficient algebra by (elementary) matrix-variables over a ground polynomial ring in not necessary commuting variables. These matrix subalgebras of full matrix rings over polynomial rings show up in noncommutative algebraic geometry. We carefully study their (one-sided or bilateral) noetherianity, obtaining a precise lift of the Hilbert Basis Theorem when the ground ring is either a commutative polynomial ring, a free noncommutative polynomial ring or a skew polynomial ring extension by a free commutative term-ordered monoid. We equally address the natural but rather delicate question of recognising which matrix polynomial algebras are Cayley-Hamilton algebras, which are interesting noncommutative algebras arising from the study of Gl--varieties.
- Subjects
MATRICES (Mathematics); ALGEBRAIC geometry; NONCOMMUTATIVE rings; MATRIX rings; COMMUTATIVE rings; NONCOMMUTATIVE algebras; POLYNOMIAL rings; CAYLEY graphs
- Publication
International Electronic Journal of Algebra, 2023, Vol 33, p137
- ISSN
1306-6048
- Publication type
Article
- DOI
10.24330/ieja.1151001