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 between an f -UP-field and an f -UP-domain. 2010 Mathematics Subject Classifications: 03G25, 08A99
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