Abstract
Characteristics of partially pseudo-ordered (K-ordered) rings are considered. Properties of the set L(R) of all convex directed ideals in pseudo-ordered rings are described. The convexity of ideals has the meaning of the Abelian convexity, which is based on the definition of a convex subgroup for a partially ordered group. It is proved that if R is an interpolation pseudo-ordered ring, then, in the lattice L(R), the union operation is completely distributive with respect to the intersection. Properties of the lattice L(R) for pseudo-lattice pseudo-ordered rings are investigated. The second and third theorems of ring order isomorphisms for interpolation pseudo-ordered rings are proved. Some theorems are proved for principal convex directed ideals of interpolation pseudo-ordered rings. The principal convex directed ideal Ia of a partially pseudo-ordered ring R is the smallest convex directed ideal of the ring R that contains the element a ∈ R. The analog for the third theorem of ring order isomorphisms for principal convex directed ideals is demonstrated for interpolation pseudo-ordered rings.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 24, No. 1, pp. 177–191, 2022.
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Mikhalev, A.V., Shirshova, E.E. Interpolation Pseudo-Ordered Rings. J Math Sci 269, 734–743 (2023). https://doi.org/10.1007/s10958-023-06310-7
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DOI: https://doi.org/10.1007/s10958-023-06310-7