Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence
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DOI: 10.1007/s10469-017-9449-2
Abstract: The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures… read more here.
Keywords: geometrical equivalence; algebraic structures; algebraic geometry; equivalence ... See more keywords
Jump Inversions of Algebraic Structures and the Σ-Definability
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DOI: 10.1007/s10469-018-9488-3
Abstract: It is proved that for every countable structure A and a successive computable ordinal α there is a countable structure A−α which is ≤Σ-least among all countable structures C such that A is Σ-definable in… read more here.
Keywords: algebraic structures; research; jump; countable structure ... See more keywords
Geometric and algebraic structures associated with the channel quantization problem
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DOI: 10.1007/s40314-017-0446-9
Abstract: We consider the use of surfaces as topological spaces in order to provide an answer to the quantization problem of a discrete memoryless channel (DMC). The aim is to identify the geometric and algebraic properties… read more here.
Keywords: algebraic structures; quantization problem; quantization; geometric algebraic ... See more keywords
Reflections in topological algebraic structures
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DOI: 10.1016/j.topol.2020.107204
Abstract: Abstract Let C be an epireflective subcategory of Top and let r C be the epireflective functor associated with C . If A denotes a (semi)topological algebraic subcategory of Top, we study when r C… read more here.
Keywords: algebraic structures; topological algebraic; question; subcategory ... See more keywords
Polyadization of Algebraic Structures
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DOI: 10.3390/sym14091782
Abstract: A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented as block diagonal matrices (resulting in the Wedderburn decomposition), general forms of polyadic structures are given by… read more here.
Keywords: polyadization algebraic; polyadization; algebraic structures; nonderived polyadic ... See more keywords