Abstract

Characteristics of partially pseudo-ordered (𝒦-ordered) algebras are considered. Properties of ideals and order homomorphisms in partially pseudo-ordered algebras are described. A variation of the concept of the prime radical for an algebra in a subclass of directed pseudo-ordered algebras (𝒜𝒪-ordered algebras) over directed fields is investigated. A description of elements of 𝒜𝒪-prime radicals for 𝒜𝒪-ordered algebras over directed fields is obtained.

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