Automorphisms of semirings and of their reducts (Q1203443)

If \(S_ 1\) and \(S_ 2\) respectively denote the additive and the multiplicative semigroup of a semiring \(S\), then the automorphism group \(\Aut(S)\) of \(S\) is, clearly, a subgroup of \(\Aut(S_ i)\) for \(i=1,2\). The paper shows that, for arbitrary groups \(G_ 1\) and \(G_ 2\) sharing a subgroup \(G\), there exists a proper class of pairwise non-isomorphic semirings \(S\) accompanied by isomorphisms \(e_ i\) of \(G_ i\) onto \(\Aut(S_ i)\) with \(i=1,2\), and such that the restrictions of \(e_ i\) to \(G\) map \(G\) isomorphically onto \(\Aut(S)\).