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In order to study the properties of SEP elements, we propose the concepts ofone sided a_idempotent and one sided a_equivalent. Under the condition that anelement in a ring is both group invertible and MP_invertible, some equivalentconditions of such an element to be an SEP element are given based on these twoconcepts, as will as based on projections and the second and the third power ofsome products of some elements.

One sided a_idempotent, one sided a_equivalent and SEP elements in a ring with involution