Scrabble?! IDEALIZER

Is idealizer valid for Scrabble? Words With Friends? Lexulous? WordFeud? Other games?
Scrabble (US/Canada)
Yes! (69 pts)
Yes! (55 pts)
Yes! (69 pts)
Yes! (69 pts)
Yes! (69 pts)
Yes! (9 pts)
Yes! (69 pts)
Yes! (71 pts)

Definitions of IDEALIZER in various dictionaries:

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

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There are 9 letters in IDEALIZER ( A1D2E1I1L1R1Z10 )

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