New posts in Semigroups

Just How Strong is Associativity?

Are these adjoint functors to/from the category of monoids with semigroup homomorphisms?

Is a semigroup $G$ with left identity and right inverses a group?

Is there an idempotent element in a finite semigroup?

Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions

Inverse elements in the absence of identities/associativity.

A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$

A finite, cancellative semigroup is a group

Eilenberg's rational hierarchy of nonrational automata & languages

Why are groups more important than semigroups?