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Glossary of ring theory
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<p> <a href="/facts/Ring_theory/VW6svEFe">Ring theory</a> is the branch of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> in which <a href="/facts/Ring_(mathematics)/JnCUXz63">rings</a> are studied: that is, structures supporting both an <a href="/facts/Addition/apFWJBFB">addition</a> and a <a href="/facts/Multiplication/VtcUjpNv">multiplication</a> operation. This is a glossary of some terms of the subject. </p><p>For the items in commutative algebra (the theory of commutative rings), see <i><a href="/facts/Glossary_of_commutative_algebra/dPjY9Aqe">Glossary of commutative algebra</a></i>. For ring-theoretic concepts in the language of modules, see also <i><a href="/facts/Glossary_of_module_theory/bFmuTYSa">Glossary of module theory</a></i>. </p><p>For specific types of algebras, see also: <i><a href="/facts/Glossary_of_field_theory/jYplty4c">Glossary of field theory</a></i> and <i><a href="/facts/Glossary_of_Lie_groups_and_Lie_algebras/6xUaAGAC">Glossary of Lie groups and Lie algebras</a></i>. Since, currently, there is no glossary on not-necessarily-associative algebra structures in general, this glossary includes some concepts that do not need associativity; e.g., a derivation. </p>