Geodesic
A generalisation of Divinsky's radical
Glasgow mathematical journal, Tome 6 (1963) no. 2, pp. 75-87

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Let A be an associative ring. Given a ∊ A, an element b ∊ A is called a left identity for a ifGiven a subset S of A, an element b ∊ A is, called a left identity for S if (1) is satisfied for all a ∊ S. An element of A need not have a left identity; for example, if A is nilpotent then no non-zero element of A has a left identity. If a does have a left identity, the latter need not be unique; if every element of a subset S of A has a left identity, then it is not necessarily true that S has a left identity. 
Bostock, F. A.; Patterson, E. M. A generalisation of Divinsky's radical. Glasgow mathematical journal, Tome 6 (1963) no. 2, pp. 75-87. doi: 10.1017/S2040618500034778
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