TITLE: Who invented Monoid?
QUESTION [10 upvotes]: I was trying to find (and failed) the original author of either

the concept of Monoid (set with binary associative operation and identity)
the name (which sounds french ? and also Dioid (for what seems to be a semiring) is exclusively french wiki article)

Question:
Is there a text source to attribute the invention of either the name or concept of monoid to a person or a group (pun intended) ?

REPLY [14 votes]: The name "monoid" was first used in mathematics by Arthur Cayley [*] for a surface of order $n$ which has a multiple point of order $n-1$.
In the context of semigroups the name is due to Bourbaki [source, page 30]

It is also worth commenting on the related term monoid, meaning an
  associative magma with identity. This term is a little more recent
  than semigroup, and seems to originate with Bourbaki [**]. Before
  this, Birkhoff (1934) was using the term groupoid for an associative
  magma with identity.

Dov Tamari [source, page 1] argues that Bourbaki "probably intended to abolish the term semigroup for reasons of linguistic taste."

[*] A. Cayley, Second and Third Memoirs on Skew Surfaces, Otherwise Scrolls, Phil. Trans. (1863 and 1869).
[**] N. Bourbaki, Éléments de Mathématique, Algèbre, Hermann, Paris (1943): Chapter I, §2.