Is there any real life application of ordered regular semigroups?

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Mohamed-Mourad Lafifi

Dear Abdous Salam,

I suggest you to see link and attached files on topic.

Regular elements in an ordered semigroup

https://msp.org/pjm/1963/13-1/pjm-v13-n1-p22-s.pdf

Best regards

Renaud Di Francesco

There are plenty of uses, as in motion, motion composition.

A more fundamental question is a specific property of group: commutation or non commutation.

Quantum mechanics relies on the uncertainty principle of Heisenberg, which can be formulated as a non-commutation of operators:

https://en.m.wikipedia.org/wiki/Canonical_commutation_relation

This is deep physics, real and usable.

Do you like photons?