Abstract
The definition of symmetric element in a ring with unity and equipped with involution can be generalized to generalized symmetric elements. But the properties of symmetric element not automatically can be generalized to generalized symmetric elements. In this paper, we discuss the property of symmetric element which can or cannot be generalized to generalized symmetric elements. Because of at least there is an element of symmetric and generalized symmetric elements which have the generalized Moore Penrose inverse, so method in this paper is by establishing a relationship between symmetric element, generalized symmetric element and generalized Moore Penrose inverse of element.
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