Geodesic
The maxit and minit of a ring
Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 128-135

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In a recent paper [2] one of the authors has introduced the concept of module type of a ring, for rings with unit. The object of this paper is to generalize this concept to arbitrary rings, without assuming the existence of a unit. This is easily accomplished for rings with one-sided unit, and we shall define the type of such a ring. Theorem 2.5 gives a relation between this type and the module type of [2], and permits the immediate extension of all results in [2] to rings with one-sided unit. 
Peinado, R. E.; Leavitt, W. G. The maxit and minit of a ring. Glasgow mathematical journal, Tome 7 (1966) no. 3, pp. 128-135. doi: 10.1017/S2040618500035310
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[1] 1.Blair, R. E., Ideal lattices and the structure of a ring, Trans. Amer. Math. Soc. 75 (1953), 136–153. Google Scholar

[2] 2.Leavitt, W. G., The module type of a ring, Trans. Amer. Math. Soc. 103 (1962), 113–130. Google Scholar

[3] 3.Jacobson, N., Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37 (Providence, R. I., 1956). Google Scholar

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