Simple (abstract algebra)
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In mathematics, the term simple is used to describe an algebraic structures which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if it contains no substructure of the same type. Some examples are:
- A group is a called simple group if it does not contain a non-trivial normal subgroup.
- A ring is called simple ring if it does not contain a non-trivial two sided ideal.
- A module is called simple module if does not contain a non-trivial submodule.
- An algebra is called simple algebra if does not contain a non-trivial two sided ideal.
