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Questions about the branch of algebra that deals with groups.

5 votes
2 answers
361 views

Have semigroups with actions on themselves that have a dual to the compatibility axiom ever ...

For a semigroup $G$ with a left action on itself, the axiom for compatibility becomes: $$ \forall f,g,h\in G:hg(f)=h(g(f)) $$ Now suppose there is additional axiom, or constraint if you prefer, call …
James Smith's user avatar
0 votes

Have semigroups with actions on themselves that have a dual to the compatibility axiom ever ...

I cannot answer the question about whether or not semigroups or monoids with consistent (what I call) self-actions have ever been studied. However, I can shed some light on consistency and its relatio …
James Smith's user avatar