On Rings with Involution and Inner Rings


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Authors

  • Azzh Saad Alshehry
  • AL Hassan AL-Jarrah
  • Rashid Abu-Dawwas
  • Ala'a AL-Kateeb

Keywords:

Rings with involution, Hermitian elements, Unitary elements, Normal elements

Abstract

In this article, we extend several known results from the ring of all $n\times n$ matrices with complex entries to any ring $R$ with nonzero unity $1$ and involution $*$. We introduce various results concerning Hermitian, skew-Hermitian, Unitary and Normal elements of $R$. Also, we propose two versions of the norm of an element and the orthogonality of two elements of $R$. Furthermore, we define an order on the elements of $R$ and examine some properties. Finally, we establish the concept of inner rings and study some of its properties.

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Published

2024-06-03

How to Cite

Alshehry, A. S., AL-Jarrah, A. H., Abu-Dawwas, R. ., & AL-Kateeb, A. (2024). On Rings with Involution and Inner Rings. Results in Nonlinear Analysis, 7(2), 79–88. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/355