Prominent GE-Filters and GE-Morphisms in GE-Algebras


The relationship between a transitive GE-algebra and a belligerent GE-algebra (also, between an antisymmetric GE-algebra and a left exchangeable GE-algebra) is displayed. A condition for the trivial GE-filter to be a belligerent GE-filter is provided. The least GE-filter containing a given GE-filter and one element is formed. Conditions under which any set can be turned into a GE-filter are described. The notions of \(\odot \)-GE-algebras and prominent GE-filters are introduced, and their properties are investigated. The relationship between a prominent GE-filter and a GE-filter are considered, and conditions for a GE-filter and the trivial GE-filter to be a prominent GE-filter are given. The conditions under which the upset of an element will be a prominent GE-filter are examined, and the extension property for the prominent GE-filter is established. The notion of GE-morphism is introduced, and the GE-morphism theorem is considered. Conditions for the kernel of a GE-morphism to be a belligerent GE-filter are provided, and the condition that if the kernel of a GE-morphism is a belligerent GE-filter, then the trivial GE-filter becomes a belligerent GE-filter is given. A condition for the kernel of a GE-morphism to be a belligerent GE-filter is discussed, and the vice versa is also considered.

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Correspondence to Ravikumar Bandaru.

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Rezaei, A., Bandaru, R., Saeid, A.B. et al. Prominent GE-Filters and GE-Morphisms in GE-Algebras. Afr. Mat. (2021).

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  • Commutative
  • Transitive
  • Left exchangeable
  • Antisymmetric
  • GE-algebra
  • GE-filter
  • Prominent GE-filter

Mathematics Subject Classification

  • 03G25c
  • 06F35