Non-Archimedean f-rings need not be p-distributive. Moreover, if {d|i} is a subset of a non-Archimedean f-ring and a ≥ 0, the elements a v d and v ad need not be equal. We prove, however, that the difference is an infinitely small element when the ring has a strong unity.
This paper deals with ordered rings and f-rings. Some relations between classes of ideals are obtained. The idea of subunity allows us to study the possibility of embedding the ring in a unitary f-ring. The Boolean algebras of idempotents and lattice-isometries in an f-ring are studied. We give geometric characterizations of the l-isometries and obtain, in the projectable case, that the Stone space of the Boolean algebra of l-isometries is homeomorphic to the space of minimal prime ideals with the...
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