On forward-order law for core inverse in rings

Abstract

If a and b are a pair of invertible elements, then ab is also invertible and the inverse of the product ab satisfyingis known as the forward-order law. This article establishes a few sufficient conditions of the forward-order law for the core inverse of elements in rings with involution. It also presents the forward-order law for the weighted core inverse and the triple forward-order law for the core inverse. Additionally, we discuss the hybrid forward-order law among the Moore-Penrose inverse, the group inverse, and the core inverse.