In group theory, the slash is used to mark quotient groups. The general form is formula_9, where formula_10 is the original group and formula_11 is the normal subgroup; this is read "formula_12 mod formula_13", where "mod" is short for "modulo". Formally this is a special case of quotient by an equivalence relation, where formula_14 iff formula_15 for some formula_16. Since many algebraic structures (rings, vector spaces, etc.) in particular are groups, the same style of quotients extend also to these, although the denominator may need to satisfy additional closure properties for the quotient to preserve the full algebraic structure of the original (e.g. for the quotient of a ring to be a ring, the denominator must be an ideal).