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Dec 30, 2016 at 3:25 comment added Gerhard Paseman The [] operation reminded me of some similar functions used in the beginnings of tame congruence theory (TCT), and a simple version of this in a monoid context is "undoing" an adjoined unit. One can imagine an iterated version undoing a succession of adjoined units, and this suggested to me operations on congruence classes, which also appears in TCT. Rather than suggest "Find an answer in TCT" (I think you won't), I suggest "Look among congruence preserving polynomial operations", where you might find a name for your relation. Gerhard "Can't Elaborate Too Much More" Paseman, 2016.12.29.
Dec 30, 2016 at 3:01 comment added goblin GONE Not quite sure I follow. Can you elaborate a little?
Dec 30, 2016 at 1:30 history answered Gerhard Paseman CC BY-SA 3.0