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A note on p-semisimple BCI-algebras. (English) Zbl 0724.06010
Let X * be the set of all endomorphisms of a p-semisimple BCI-algebra (X,·,0) and let M and N be nonempty sets such that MX, NX * . Then X * is a p-semisimple BCI-algebra and M ={x * X * : x * (x)=0 for all xM}, N={xX: x * (x)=0 for all x * N} are closed weakly implicative ideals. Moreover, for any homomorphism T: XX there corresponds a unique homomorphism T * :X * * such that x * (Tx)=T * x * (x). In this case Ker(T * )=R(T) and Ker(T)= R(T * ), where Ker and R denote the kernel and the range of the homomorphism, respectively.

MSC:
06F35BCK-algebras, BCI-algebras
03G25Other algebras related to logic