Browsing by Author "Mahawanniarachchi, Padmal Sathyajith"

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    P-algebras and Q-algebras
    (University of Alabama Libraries, 2010) Mahawanniarachchi, Padmal Sathyajith; Neggers, Joseph; University of Alabama Tuscaloosa
    We define two classes of algebras P- and Q-, which are derived from the definitions of BCK- and BCI- algebras. The birth of P-algebras is based on the symmetric difference in set theory. We prove that the class of P-algebras is a variety, and the definition of P-algebras is an alternative definition for groups of exponent 2, which we call P-groups. The class of Q-algebras consists of a combination of three axioms of BCK- and P- algebras. We study the relationship among P-, Q- and BCI- algebras. The theory of P- and Q- algebras is developed parallel to the theory of BCK- and BCI- algebras.