On properties of square-free elements in commutative cancellative monoids (Q2182460)

Let \(H\) be a monoid, \(M\subseteq H\) a submonoid and \(\Lambda(H)\) the set of all atoms in \(H\), \(S(H)\) the set of all square-free elements in \(H\). The authors discuss square-free factorizations in monoids in the paper and discuss the connections with the Jacobian conjecture in Section 2. Then they give the sufficient conditions for \(\Lambda(M)\subseteq S(H)\) in Section 4 and give some equivalent statements for \(S(M)\subseteq S(H)\) in Section 5. Finally, they discuss the radical elements in a monoid and classify the monoids with respect to square-free factorizations.