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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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On rings $R$ for which $R \cong \frac RI$ for any proper two-sided ideal $I$
This is a problem I asked in SE, but it seems the question is more suitable for MO.
Consider a ring $R$ (not necessary with identity or commutative) such that for any proper two-sided ideal $I$, $R\ …