Degree estimate for subalgebras
Copyright policy )Degree estimate for subalgebras
Based on Bergman's Lemma on centralizers, we obtain a sharp lower degree bound for nonconstant elements in a subalgebra generated by two elements of a free associative algebra over an arbitrary field.
10 pages
- University of Hong Kong China (People's Republic of)
- The University of Hong Kong China (People's Republic of)
- University of Hong Kong (香港大學) China (People's Republic of)
Centralizers, free associative algebras, degree estimates, subalgebras, Degree estimate, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Primary 13S10, 16S10. Secondary 13F20, 13W20, 14R10, 16W20, 16Z05, Subalgebras, commutators, ordered groups, centralizers, FOS: Mathematics, Free associative algebras, Mal'cev-Neumann algebras, Malcev–Neumann algebras, Automorphisms and endomorphisms, Algebra and Number Theory, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Mathematics - Rings and Algebras, Commutators, Computational aspects of associative rings (general theory), Polynomial rings and ideals; rings of integer-valued polynomials, Rings and Algebras (math.RA), Ordered groups
Centralizers, free associative algebras, degree estimates, subalgebras, Degree estimate, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Primary 13S10, 16S10. Secondary 13F20, 13W20, 14R10, 16W20, 16Z05, Subalgebras, commutators, ordered groups, centralizers, FOS: Mathematics, Free associative algebras, Mal'cev-Neumann algebras, Malcev–Neumann algebras, Automorphisms and endomorphisms, Algebra and Number Theory, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Mathematics - Rings and Algebras, Commutators, Computational aspects of associative rings (general theory), Polynomial rings and ideals; rings of integer-valued polynomials, Rings and Algebras (math.RA), Ordered groups
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