Abstract
In this chapter, we define formal matrix rings of order 2 and formal matrix rings of arbitrary order n. Their main properties are considered and examples of such rings are given. We indicate the relationship between formal matrix rings, endomorphism rings of modules, and systems of orthogonal idempotents of rings. For formal matrix rings, the Jacobson radical and the prime radical are described. We find when a formal matrix ring is Artinian, Noetherian, regular, unit-regular, and of stable rank 1. In the last section, clean and k-good matrix rings are considered.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Krylov, P., Tuganbaev, A. (2017). Formal Matrix Rings. In: Formal Matrices. Algebra and Applications, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-53907-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-53907-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-53906-5
Online ISBN: 978-3-319-53907-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)