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I want to coalesce multiple operations in a system into one and am currently studying under what conditions it is admissible. The conditions that are needed are stronger than idempotence and I'm wondering if it has well-known name:

E.g.: considers two operations assigning a variable A: x ← 1 and B: x ← 2. Both are idempotent.

By idempotence, we can conclude various things about sequential composition of those operations:

A * A = A
A * A * B * B = A * B

But we cannot use idempotence to get A * B = B even though that's of course true given the definitions of A and B.

How would you name or concisely describe this compositional property of the operations?

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This sounds a bit like absorption. But I'm not quite sure this is exactly what you need.

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