Some results in hyper BCK-Algebras - Amancio, Jennybeth L.; Manzano, Ramises Jr. (Cebu City College of Science, University of the Philippines Cebu, 2022)
BCK-algebra has been studied lately by various mathematicians. It is viewed as a generalization of the notion of algebra sets with the subtraction set with only a fundamental, non-nullary operation and the notion of implication algebra on the other hand. Jun, Zahedi, Xin and Borzooei applied the hyperstructures to BCK-algebras, and introduced the notion of a hyper BCK-algebra which is a generalization of BCK-algebra, and investigated some related properties. In this paper, first, we define the notions of positive implicative hyper BCK-ideals of types 1,2,3,4,5,6,7,and 8, study conditions for a hyper BCK-ideal to be a positive implicative BCK-ideal and investigate some related properties. Next, giving some examples, we show that these notions are different. Then,we establish some homomorphism theorems on hyper BCK-algebra. After that, we investigate some related properties about the concept of regular congruence relation on hyper BCK-algebras and construct a quotient hyper BCK-algebra H/I via regular congruence. Finally, we state and prove the First Isomorphism Theorem and Third Isomorphism Theorem for hyper BCK-algebras.
Thesis (Bachelor of Science in Mathematics)--University of the Philippines Cebu, June 2022.
Keywords: Algebra