Geodesic
Convex ideals of partially pseudo-ordered rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 3, pp. 181-199.

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Characteristics of partially pseudo-ordered ($K$-ordered) rings are considered. Properties of the set of all convex directed ideals in pseudo-ordered rings are described. It is shown that convex directed ideals play for the theory of partially pseudo-ordered rings the same role as convex directed subgroups for the theory of partially ordered groups. Necessary and sufficient conditions for a convex directed ideal of an $AO$-pseudo-ordered ring to be a rectifying ideal are obtained. We show that the set of all rectifying directed ideals of an $AO$-pseudo-ordered ring form the root system for the lattice of all convex directed ideals of that ring. Properties of regular ideals for partially pseudo-ordered rings are investigated. Some results are proved concerning convex directed ideals of pseudo-lattice pseudo-ordered rings. 
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E. E. Shirshova. Convex ideals of partially pseudo-ordered rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 3, pp. 181-199. http://geodesic.mathdoc.fr/item/FPM_2023_24_3_a10/

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