Is there a name for an object $L$ that has an additive structure and a (not necessarily total) order such that for all $a,b,c \in $ L we have
- $a+b = b+a$
- $a+(b+c)= (a+b)+c $
- $a+b \leq a+c \Leftrightarrow b \leq c$
2026-04-18 23:39:18.1776555558
What is this algebraic structure called like?
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Well, the structure is a commutative and ordered semigroup.