On Rings with Involution and Inner Rings
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Keywords:
Rings with involution, Hermitian elements, Unitary elements, Normal elementsAbstract
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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