Geodesic
On Lifting Idempotents
Canadian mathematical bulletin, Tome 17 (1974) no. 4, p. 607

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Let N be an ideal of a ring A. We say that idempotents modulo N can be lifted provided that for every a of A such that a2-a ∈ N there exists an element e2=e ∈ A such that e-a ∈ N. The technique of lifting idempotents is considered to be a fundamental tool in the classical theory of nonsemiprimitive Artinian rings (refer [2; p. 72]). 
Koh, Kwangil. On Lifting Idempotents. Canadian mathematical bulletin, Tome 17 (1974) no. 4, p. 607. doi: 10.4153/CMB-1974-111-5
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[1] 1. Jacobson, N., Structure of Rings, American Mathematical Society Colloquium, Vol. 36, Rev. ed. Providence, R.I.: 1964. Google Scholar

[2] 2. Lambek, J., Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham, Massachusetts: 1966. Google Scholar

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