Geodesic
Characterizing f-rings
Glasgow mathematical journal, Tome 16 (1975) no. 2, pp. 88-90

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Birkhoff and Pierce [2] introduced the class f-rings—those lattice-ordered rings R which satisfy the additional condition that if a, b, and c are positive elements of R and if a ∧ b = 0, then ac ∧ b = 0 = ca ∧ b. They showed that f-rings may be characterized as lattice-ordered rings which are subdirect products of totally-ordered rings. 
Colville, Peter D. Characterizing f-rings. Glasgow mathematical journal, Tome 16 (1975) no. 2, pp. 88-90. doi: 10.1017/S0017089500002561
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