Consider a quasigroup $(Q,/)$, that is, Q is any set and for $\forall a,b\in Q$ there are unique solutions to the equations $x/a=b$ and $a/y=b$. How to find a maximal set of independent identities of ...
In other words what do we call a magma which is associative and has divisibility property but not existence of identity? Or a groupoid when it loses the identity property? A reference on such ...
A partial binary operation on a set $X$ is just a (partial) function $\varphi: X \times X \rightharpoonup X$ (I'm using \rightharpoonup for partial maps), and a partial magma is a pair $\mathbb M = ...
Wikipedia credits Bourbaki with coining it, but doesn't provide a source. Does anyone happen to know the motivation for using this term?
Arguably the most import thing about groups, semigroups and more generally categories, is that they can act on sets (or even collections of sets in the case of a category). This is the basis for all ...
BOURBAKI, inside his book on ALGEBRA defines and provides explicit constructions concerning the concepts of free magma, free monoid (and implicitly free semi-group) and free group, and as well free ...