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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Matrix wreath products of algebras and embedding theorems


Authors: Adel Alahmadi, Hamed Alsulami, S. K. Jain and Efim Zelmanov
Journal: Trans. Amer. Math. Soc. 372 (2019), 2389-2406
MSC (2010): Primary 16-XX
DOI: https://doi.org/10.1090/tran/7642
Published electronically: May 20, 2019
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Abstract: We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §6, we construct finitely generated nil algebras of arbitrary Gelfand-Kirillov dimension $ \geq 8$ over a countable field which answers a question from [New trends in noncommutative algebra, Amer. Math. Soc., Providence, RI, 2012, pp. 41-52].


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Additional Information

Adel Alahmadi
Affiliation: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Email: analahmadi@kau.edu.sa

Hamed Alsulami
Affiliation: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Email: hhaalsalmi@kau.edu.sa

S. K. Jain
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: jain@ohio.edu

Efim Zelmanov
Affiliation: Department of Mathematics, University of California, San Diego, Lagolla, California 92093-0112
Email: ezelmano@math.ucsd.edu

DOI: https://doi.org/10.1090/tran/7642
Keywords: Associative algebra, wreath products, finitely generated algebra
Received by editor(s): January 17, 2018
Received by editor(s) in revised form: March 4, 2018, and March 10, 2018
Published electronically: May 20, 2019
Additional Notes: The fourth author is the corresponding author. The fourth author gratefully acknowledges the support from NSF grant 1601920.
The authors designed research, performed research, and wrote the paper. The authors declare no conflict of interest.
Article copyright: © Copyright 2019 American Mathematical Society