00000ctm a22000003a 4500 UP-8027390931312570363 Buklod 20240802141755.0 o--- | || || ta 240802s2022 xx d r |||| u| (iLib)UPCEB-00013239882 UPC eng LG 993.5 2022 M38 D34 Daguplo, Adrian Dave author. On Hyper BCC-algebras Adrian Dave Daguplo, Ramises G. Manzano, Jr., thesis adviser. Cebu City College of Science, University of the Philippines Cebu 2022. x, 93 leaves illustrations Thesis (Bachelor of Science in Mathematics)--University of the Philippines Cebu, June 2022. Yes-Available to the general public. No-Available only after consultation with author/adviser for thesis. No-Available only to those bound by non-disclosure or confidentiality agreement. P-the author wishes to publish the work personally Hyper BCC-algebras has been studied by Borzooei, et al. [4]. They are viewed as a generalization of BCC-algebras and hyper BCK-algebras. This paper presents the notions of hyper BCC-algebras and some of their properties and shows their relationships with the other algebraic structures and hyper algebras. Also, this investigates the different types of hyper BCC-ideals and the relationships of hyper BCK-ideals, weak hyper BCK-ideals, and strong hyper BCK-ideals to some of the types of hyper BCC-ideals and hyper subBCC-algebra. Extending the notion of hyper BCC-algebras, this formulates the concepts of hyper BCC-algebra hyper homomorphism and hyper BCC-algebra quotient structure of hyper BCC-algebras. Results show that any hyper BCK-algebra is a hyper BCC-algebra. However, the converse is not true in general, that is, only some of the hyper BCC-algebras are hyper BCK-algebras. It is illustrated that a subset S (H) of a hyper BCC-algebra H is a BCC-algebra. Similarly, a hyper BCC-algebra H is also a BCK-algebra. Further results show that the subset I of H such that 0 ∈ I is a hyper BCC-ideal of types 1, 2, 3, and/or 4. A Hyper BCK-ideal I of H is shown to be a hyper BCC-ideal of type 1. Similarly, a weak hyper BCK-ideal I of H is shown to be a hyper BCC-ideal of type 2. A strong hyper BCK-ideal I of H is a hyper subBCC-algebra of hyper BCC-algebras. Additionally, it is proven that a function f mapping two hyper BCC-algebras H and H′ is a hyper BCC-algebra hyper homomorphism of hyper BCC-algebras. If f is one-to-one, then it is a hyper BCC-algebra hyper monomorphism and if f is onto, then it is a hyper BCC-algebra hyper epimorphism. Moreover, a hyper BCC-algebra H with a well-defined θ-regular congruence relation can formulate a hyper BCC-algebra quotient structure H/I of hyper BCC-algebras. Algebra. Manzano, Ramises Jr. thesis adviser. UP UPCEB CEBU-LAHUG LG 993.5 2022 M38 D34 Thesis