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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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Special element of a commutative ring
Let $R$ be a commutative ring with $1$ and $S $ be a multiplicative subset of $R $. I am looking for an equivalence condition for the following property in $R $:
Property: There exists a fixed el …