HOW TO NAVIGATE SEMI GROUPS?So since semi-groups are irreversible, commutators and conjugates don't work for them. With these methods, you can navigate groups easily. What's the equivalent thing for semi groups that works? What tools do you use?
>>17034386well if it is finitely generated you can use the generators. If it isn't, you have infinite strings with infinite alphabets, what structure could possibly be left?
>>17034386>So since semi-groups are irreversibleTime and momentum are symmetrical forwards and backwards. So, irreversibility is merely an illusion of the third dimension.
To the 1st reply: Once you have the generators, what can you do with them? I know they give very important information, but what next? Sorry that I'm so uninformed, I'm trying my best : (
>>17034794The problem is, most of the time generators help you reason about even infinite groups by proving properties for the generators and then showing that products of generators retain them. For semi groups, almost nothing remains that is this generic that I am aware of. I would strongly suggest for you to study finite groups of low order and then look at finite semigroups of low order that aren't groups. Explore, try to see if you can force some theorems or properties you find for small fininte groups to hold for the remaining semi groups. Compare the different kinds of magmas side by side. It will teach you a lot. Then dig into the lit.
