New posts in Semigroups

Is a monoid commutative if $(ab)^2=a^2b^2$?

In a Cayley table, which Group axioms fail when an entry appears twice in a row or a column?

Show that a semigroup with $aS \cup \{a\} = bS \cup \{b\}$ and $Sa \cup \{a\} = Sb \cup \{b\}$ is a group

Is this structure a group?

The set of primes of the form $a^2+8b^2$, where $a,b\in\mathbb N_+$

Definition of groups

Does associativity imply closure?

Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$?

Does a non-abelian semigroup without identity exist?

Is there a name for a regular semigroup with zero in which the product of any two different idempotents is zero?