is then an area ring with the maximal ideal p R p displaystyle mathfrak p R_ mathfrak p
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the aspect or perception offered by a statement, an action, and so on., taken as revealing a specified inherent good quality: a ring of assurance in her voice; the ring of reality; a false ring.
and a component x in S there exists a unique ring homomorphism ϕ ¯ : R [ t ] → S displaystyle overline phi :R[t]to S
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Additive functors involving preadditive categories generalize the principle of ring homomorphism, and ideals in additive types could be defined as sets of morphisms shut under addition and beneath composition with arbitrary morphisms. Generalization
. From the Artin–Wedderburn theorem, a central simple algebra will be the matrix ring of a division ring; So, Each and every similarity course is represented by a unique division ring.
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A noteworthy instance is a Lie algebra. There exists some framework theory for this sort of algebras that generalizes the analogous effects for Lie algebras and associative algebras.[citation desired] Semiring
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