(untitled) (European Journal of Pure and Applied Mathematics, 2019)
This paper investigates a new class of algebra related to UP-algebras and semigroups called fully UP-semigroups (or f-UP-semigroups). It establishes some structural properties of f-UP-semigroups. It also introduces and examines f-UP-fields, f-UP-domains, f-UP-ideals, and quotient f-UP-semigroups. Moreover, it investigates the relationship betweenÂ an f-UP-field and an f-UP-domain.