Characterizations of semihoops based on derivations

In this paper, we discuss the related properties of some particular derivations in semihoops and give some characterizations of them. Then, we prove that every Heyting algebra is isomorphic to the algebra of all multiplicative derivations and show that every Boolean algebra is isomorphic to the algebra of all implicative derivations. Finally, we show that the sets of multiplicative and implicative derivations on bounded regular idempotent semihoops are in one-to-one correspondence.