Subring Generated By A Set
Let R be a ring. Any intersection of subrings of R is again a subring of R. Therefore, if X is any subset of R, the intersection of all subrings of R containing X is a subring S of R. S is the smallest subring of R containing X. ("Smallest" means that if T is any other subring of R containing X, then S is contained in T.) S is said to be the subring of R generated by X. If S = R, we may say that the ring R is generated by X.
Read more about this topic: Subring Test
Famous quotes containing the words generated and/or set:
“It is precisely the purpose of the public opinion generated by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.”
—Walter Benjamin (1892–1940)
“One does not set fire to a world which is already lost.”
—Friedrich Dürrenmatt (1921–1990)