Geodesic
Quotient Rings of a Class of Lattice-Ordered-Rings
Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 627-645

Voir la notice de l'article provenant de la source Cambridge University Press

An f-ring R with zero right annihilator is called a qf-ring if its Utumi maximal left quotient ring Q = Q(R) can be made into and f-ring extension of R. F. W. Anderson [2, Theorem 3.1] has characterized unital qf-rings with the following conditions: For each q ∈ Q and for each pair d1, d2 ∈ R + such that d i q ∈ R(i) (d1q)+ Λ (d2q)- = 0, and(ii) d1 Λ d2 = 0 implies (d1q)+ Λ d2 = 0.We remark that this characterization holds even when R does not have an identity element. 
Steinberg, Stuart A. Quotient Rings of a Class of Lattice-Ordered-Rings. Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 627-645. doi: 10.4153/CJM-1973-064-3
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