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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 3, pp. 215–230, 2020.
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Mikhalev, A.V., Shirshova, E.E. Prime Radicals of Directed Pseudo-Ordered Algebras Over Directed Fields. J Math Sci 269, 411–421 (2023). https://doi.org/10.1007/s10958-023-06289-1
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DOI: https://doi.org/10.1007/s10958-023-06289-1