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International Journal of Mathematics Trends and Technology, vol.70, no.6, pp.13-19, 2024 (Peer-Reviewed Journal)
In this study, by using the set of the source of semiprimeness, we give the definitions of |𝑆𝑆|− inverse semigroup and |𝑆𝑆|− inverse monoid which are generalizations of semigroup and monoid concepts. Then, we investigate these structures and determine their basic properties. Then, we define |𝑆𝑆|− group using these definitions. Using the definitions given, we examine the relationships between the new structures.