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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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Quotient of a ring by a left ideal

This is a simple algebra question I'm struggling with. Let $A$ be a ring (with unity) and $I\subset A$ a left ideal and $B\subset A$ a two sided Ideal. $A/I=B$ and $A/B=I$ (in the category of left $A …
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