Abstract
In a ring with involution we already know that the Moore Penrose inverse can be used to construct the properties of normal elements. By using the fact that the group inverse of an element in a ring will be commutative with element which is commutative with that element, this paper explains that the generalization of Moore Penrose inverse can be also to establish some properties of normal elements in a ring with an involution. Some elements in the ring such as symmetric, EP, partial isometries, etc are also can be expressed in group inverse. So the results of this paper much be required for built the properties of those elements.
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