Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A matrix representation for associative algebras. I


Author: Jacques Lewin
Journal: Trans. Amer. Math. Soc. 188 (1974), 293-308
MSC: Primary 16A64; Secondary 16A42
MathSciNet review: 0338081
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let F be a mixed free algebra on a set X over the field K. Let U, V be two ideals of F, and $ \{ \delta (x),(x \in X)\} $ a basis for a free $ (F/U,F/V)$-bimodule T. Then the map $ x \to (\begin{array}{*{20}{c}} {x + V} & 0 \\ {\delta (x)} & {x + U} \\ \end{array} )$ induces an injective homomorphism $ F/UV \to (\begin{array}{*{20}{c}} {F/V} & 0 \\ T & {F/U} \\ \end{array} )$. If $ F/U$ and $ F/V$ are embeddable in matrices over a commutative algebra, so is $ F/UV$. Some special cases are investigated and it is shown that a PI algebra with nilpotent radical satisfies all identities of some full matrix algebra.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A64, 16A42

Retrieve articles in all journals with MSC: 16A64, 16A42


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0338081-5
PII: S 0002-9947(1974)0338081-5
Keywords: Free algebra, universal derivation, embedding in matrices, matrix identities, Noetherian PI algebras, Abelian-by-nilpotent groups
Article copyright: © Copyright 1974 American Mathematical Society