GE-filters, ordering filters and left mappings in GE-algebras

Abstract

The notions of ordering filter and left mapping in a GE-algebra are introduced, and their properties are investigated. Relations between ordering filters and GE-filters are established. Conditions for an ordering filter to be a GE-filter, and vice versa, are provided. The conditions under which a left mapping becomes injective or an identity are explored. The conditions under which the GE-kernel of a self-mapping will be a GE-filter are provided. It is confirmed that the sets of all left mappings form a semigroup, and that the sets of all idempotent left mappings form a subsemigroup. The conditions under which the sets of all left mappings can be closed with respect to a binary operation are investigated.

Keywords

• GE-filter
• ordering filter
• idempotent left mapping
• GE-kernel

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