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)]]