Abstract
ABSTRACTWe define and investigate the e-core inverse and f-dual core inverse in a ring with involution as extensions of the core and dual core inverse, respectively. Using these definitions, we present and characterize the e-core partial order and the f-dual core partial order. We describe the sets of all elements a Rickart ∗-ring which are below a given element under the e-core and f-dual core partial order. New characterizations of weighted-EP elements are given too.
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