Database of Ring Theory
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Theorems in ring theory
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All theorems
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About ideals
Characterization of properties
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Properties of special subsets
Theorems illustrating properties and interrelationships between special subsets.
$\mathcal Z(R_R)\subseteq \ell.ann(soc(R_R))$, and they are equal when $R$ is right Artinian.
$J(R)=\mathcal Z(R_R)$ for principally injective rings
$Nil_\ast(R)\subseteq Nil^\ast(R)\subseteq J(R)$
$soc(_RR)=soc(R_R)$ in dual rings
Amitsur's nil radical theorem
Nilpotency of $\mathcal Z(R_R)$
Socles coincide in semiprime rings