"Levi's Commutator Theorems for Cancellative Semigroups"
R. Padmanabhan, W. McCune, R. Veroff
Semigroup Forum, vol. 71, , pp. 152-157. Also Preprint ANL/MCS-P1192-0804
Preprint Version: [pdf]
Levi's commutator theorems in group theory are generalized to cancellative semigroups. The theorems involve associativity, distributivity, and class two nilpotence of commutator expressions. The cancellative semigroup theorems are proved by automated deduction. The work is related to conjecture of Padmanabhan, that is, if a certain class of statement is provable in group theory, then it is also provable in cancellative semigroups.