simple

Algebraic structure which cannot be divided

ConceptconceptQ2315394

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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 it does not contain a nontrivial submodule. An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal.

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Facet of: abstract algebra
Different from: Simpla criterion used: descriptive page and disambiguation page have to be in different items · applies to name of object: simpla
Simple criterion used: descriptive page and disambiguation page have to be in different items · applies to name of object: simple

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Source last edited September 8, 2026. AIDB refreshes this page daily.

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AIDB. (2026). simple (Q2315394). Retrieved from https://aidb.si/e/simple-Q2315394