We introduce and study a new class of generalized inverses in rings. An element 𝑎 in a ring 𝑅 has p-Hirano inverse if there exists 𝑏 ∈ 𝑅 such that 𝑏𝑎𝑏 = 𝑏, 𝑏 ∈ 𝑐𝑜𝑚𝑚2(𝑎), (𝑎2 - 𝑎𝑏)𝑘 ∈ ...
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