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Interpolation Pseudo-Ordered Algebras Over Partially Ordered Fields
Characteristics of partially pseudo-ordered ( K -ordered) algebras over partially ordered fields are considered. Properties of the set L ( A ) of all...
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Injective Hulls are Completions of Ordered Algebras
It is well-known that the Dedekind-MacNeille completion of a poset is its injective hull. We prove that the injective hull of an ordered universal...
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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...
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Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra
Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown...
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The construction of fuzzy linguistic attribute partial ordered structure diagram
In formal concept analysis, as a data visualization tool, attribute partial ordered structure diagram can effectively discover the partial order...
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Interpolation Pseudo-Ordered Rings
Characteristics of partially pseudo-ordered ( K -ordered) rings are considered. Properties of the set L ( R ) of all convex directed ideals in...
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Ordered Vector Spaces and Positivity
This chapter is a pragmatic review of the basic theory of ordered vector spaces. Among other things, we present the notion of positive linear...
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Adjunction of a strong unit to a hyper-archimedean lattice-ordered group
This paper studies conditions in which a hyperarchimedean lattice-ordered group embeds into a hyperarchimedean lattice-ordered group with strong...
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Algebra
The language of spectral theory is algebra, so we should begin with some kind of dictionary.
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Time-like definition of quaternions in exterior algebra
A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three...
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Linear map**s on ordered vector spaces
Before we can start to analyze the generalized Riccati operators derived in the previous chapter, we have to deal with generalized Lyapunov operators...
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Real Algebra A First Course
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of...
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Maximal Ordered Groupoids and a Galois Correspondence for Inverse Semigroup Orthogonal Actions
We introduce maximal ordered groupoids and study some of their properties. Also, we use the Ehresmann–Schein–Nambooripad Theorem, which establishes a...
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Linear Algebra
Linear algebra introduces students to abstract concepts associated with vectors and matrices. Some students may have already worked with matrices at...
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Varieties of ordered algebras as categories
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category...
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Idempotents in the Endomorphism Algebra of a Finite Lattice
We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T . This idempotent is associated with...