Prime Radicals of Directed Pseudo-Ordered Algebras Over Directed Fields

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-order...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-01, Vol.269 (3), p.411-421
Main Authors: Mikhalev, A. V., Shirshova, E. E.
Format: Article
Language:English
Subjects:
Algebra
Homomorphisms
Mathematics
Mathematics and Statistics
Radicals
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06289-1