Fixed-point subring

In algebra, the fixed-point subring of an automorphism f of a ring R is the subring of the fixed points of f:

More generally, if G is a group acting on R, then the subring of R:

is called the fixed subring or, more traditionally, the ring of invariants. In Galois theory, when R is a field and G is a group of field automorphisms, the fixed ring is a subfield called the fixed field of the automorphism group; see Fundamental theorem of Galois theory.