Geodesic
The Jacobson Radical and Regular Modules
Canadian mathematical bulletin, Tome 18 (1975) no. 1, p. 141

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Let A be an associative, but not necessarily commutative, ring with identity, and J = J(A) its Jacobson radical. A (unital) module is regular iff every submodule is pure (see (1)). The regular socle R(M) of a module M is the sum of all its submodules which are regular. These concepts have been introduced and studied in (2). 
Fieldhouse, David J. The Jacobson Radical and Regular Modules. Canadian mathematical bulletin, Tome 18 (1975) no. 1, p. 141. doi: 10.4153/CMB-1975-026-5
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[1] 1. Cohn, P. M., On the free product of associative rings, I, Math. Z. 71 (1959) 380-398. Google Scholar

[2] 2. Fieldhouse, D., Pure Theories, Math. Annalen 184 (1969) 1-18. Google Scholar

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