Extending an Established Isomorphism between Group Rings and a Subring of the n × n Matrices

Electronic version of an article published as International Journal of Algebra and Computation, Volume 31, Issue 3, 2021, Pages 471-490. [https://doi.org/10.1142/S0218196721500223] © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijacIn this work, we extend an established isomorphism between group rings and a subring of the n × n matrices. This extension allows us to construct more complex matrices over the ring R. We present many interesting examples of complex matrices constructed directly from our extension. We also show that some of the matrices used in the literature before can be obtained by a direct application of our extended isomorphism