About: (mathematics) A way in which each element of some algebraic structure transforms some other structure or set, in a way which respects the structure of the first. Formally, this may be seen as a morphism from the first structure into some structure of endomorphisms of the second; for example, a group action of a group G on a set S can be seen as a group homomorphism from G into the set of bijections on S (which form a group under function composition), while a module M over a ring R can be defined as an abelian group together with a ring homomorphism from R into the ring of group endomorphisms of M (which is also called the action of R on M).       Sponge   NotDistinct   Permalink