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idealizer
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Definitions of idealizer in various dictionaries:
IDEALIZER - In abstract algebra, the idealizer of a subsemigroup T of a semigroup S is the largest subsemigroup of S in which T is an ideal. Such an idealizer is...
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| A person who idealizes |
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In abstract algebra, the idealizer of a subsemigroup T of a semigroup S is the largest subsemigroup of S in which T is an ideal. Such an idealizer is given by* * * * * * I * * * S * * * ( * T * ) * = * { * s * * S * * s * T * * T * * and * * T * s * * T * } * * * {\displaystyle \mathbb {I} _{S}(T)=\{s\in S\mid sT\subseteq T{\text{ and }}Ts\subseteq T\}} * In ring theory, if A is an additive subgroup of a ring R, then * * * * * * I * * * R * * * ( * A * ) * * * {\displaystyle \mathbb {I} _{R}(A)} * (defined in the multiplicative semigroup of R) is the largest subring of R in which A is a two-sided ideal.In Lie algebra, if L is a Lie ring (or Lie algebra) wi |