Editing Modulo (mathematics) (section)

===Structures===
The term "modulo" can be used differently—when referring to different mathematical structures. For example:
* Two members ''a'' and ''b'' of a [[group (mathematics)|group]] are congruent modulo a [[normal subgroup]], [[if and only if]] ''ab''<sup>−1</sup> is a member of the normal subgroup (see [[quotient group]] and [[isomorphism theorem]] for more).
* Two members of a [[ring (mathematics)|ring]] or an algebra are congruent modulo an [[ideal (ring theory)|ideal]], if the difference between them is in the ideal.
** Used as a verb, the act of [[Quotient group|factoring]] out a normal subgroup (or an ideal) from a group (or ring) is often called "''modding out'' the..." or "we now ''mod out'' the...".
* Two subsets of an infinite set are '''equal modulo finite sets''' precisely if their [[symmetric difference]] is finite, that is, you can remove a finite piece from the first subset, then add a finite piece to it, and get the second subset as a result.
* A [[short exact sequence]] of maps leads to the definition of a [[Quotient space (topology)|quotient space]] as being one space modulo another; thus, for example, that a [[cohomology]] is the space of [[differential form|closed forms]] modulo exact forms.