## Matrix wreath products of algebras and embedding theorems

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- by Adel Alahmadi, Hamed Alsulami, S. K. Jain and Efim Zelmanov PDF
- Trans. Amer. Math. Soc.
**372**(2019), 2389-2406 Request permission

## 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
- MR Author ID: 771392
- ORCID: 0000-0002-7758-3537
- 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
- MR Author ID: 199020
- Email: jain@ohio.edu
**Efim Zelmanov**- Affiliation: Department of Mathematics, University of California, San Diego, Lagolla, California 92093-0112
- MR Author ID: 189654
- Email: ezelmano@math.ucsd.edu
- 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. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**372**(2019), 2389-2406 - MSC (2010): Primary 16-XX
- DOI: https://doi.org/10.1090/tran/7642
- MathSciNet review: 3988580