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In mathematics, the term simple is used to describe an algebraic structure 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 of every homomorphism is either the whole structure or a single element. Some examples are: * A group is called a simple group if it does not contain a nontrivial proper normal subgroup. * A ring is called a simple ring if it does not contain a nontrivial two sided ideal. * A module is called a simple module if does not contain a nontrivial submodule. * An algebra is called a simple algebra if does not contain a nontrivial two sided ideal. The general pattern is that the structure admits no non-trivial congruence relations. The term is used differently in semigroup theory. A semigroup is said to be ''simple'' if it has no nontrivial ideals, or equivalently, if Green's relation ''J'' is the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may have nontrivial congruences. A semigroup with no nontrivial congruences is called ''congruence simple''. ==See also== * semisimple 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Simple (abstract algebra)」の詳細全文を読む スポンサード リンク
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