Semigroup Isomorphism/Examples

Examples of Semigroup Isomorphisms

Structure with Two Operations

Let $\struct {S_1, \circ_1, *_1}$ and $\struct {S_2, \circ_2, *_2}$ be algebraic structures such that:

$\struct {S_1, \circ_1}$ is isomorphic to $\struct {S_2, \circ_2}$

$\struct {S_1, *_1}$ is isomorphic to $\struct {S_2, *_2}$

Then it is not necessarily the case that $\struct {S_1, \circ_1, *_1}$ is isomorphic to $\struct {S_2, \circ_2, *_2}$.