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Characterizing f-rings
Published online by Cambridge University Press: 18 May 2009
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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.
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- Copyright © Glasgow Mathematical Journal Trust 1975
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