Simple (abstract algebra)
3875683
188645235
2008-02-02T19:12:28Z
Michael Slone
279360
add indefinite articles
In [[mathematics]], the term '''simple''' is used to describe an [[algebraic structure]]s which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the [[Kernel (algebra)|kernel]] of every homomorphism is either the whole structure or a single element. Some examples are:
* A [[group (mathematics)|group]] is a called a [[simple group]] if it does not contain a non-trivial proper [[normal subgroup]].
* A [[ring (mathematics)|ring]] is called a [[simple ring]] if it does not contain a non-trivial [[two sided ideal]].
* A [[module (mathematics)|module]] is called a [[simple module]] if does not contain a non-trivial [[submodule]].
* An [[algebra (mathematics)|algebra]] is called a [[simple algebra]] if does not contain a non-trivial [[two sided ideal]].
The general pattern is that the structure admits no non-trivial [[Congruence_relation#Universal_algebra|congruence relations]].
== See also ==
* [[semisimple]]
[[Category:Abstract algebra]]
[[eo:Simpla (abstrakta algebro)]]