Geodesic
Interpolation pseudo-ordered rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 177-191

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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 $I_a$ of a partially pseudo-ordered ring $R$ is the smallest convex directed ideal of the ring $R$ that contains the element $a\in R$. 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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     author = {A. V. Mikhalev and E. E. Shirshova},
     title = {Interpolation pseudo-ordered rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {177--191},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2022_24_1_a5/}
}
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A. V. Mikhalev; E. E. Shirshova. Interpolation pseudo-ordered rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2022) no. 1, pp. 177-191. http://geodesic.mathdoc.fr/item/FPM_2022_24_1_a5/