# Tagged Questions

A semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup with an identity element is called monoid. This tag is most frequently used for questions related to the concept of semigroups in the context of abstract algebra. Please use the more ...

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### What can we learn about a magma by studying these monoids?

Given a magma $(X,*)$, we get three monoids in the following way. First, define a pair of functions $L,R : X \rightarrow (X \rightarrow X).$ $$(Lx)(y) = x*y,\quad (Rx)(y) = y*x$$ Then each of the ...
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### Does Cartesian Product and Collection of all Sets Perform a Semigroup?

We know that the Cartesian Product is a binary operation. Also it is an associative operation. We know that Cartesian Product of two set is again set, there is even closure axiom. So I need to know ...
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### If a semigroup satisfies these identities, is it necessarily commutative?

Suppose a semigroup $X$ satisfies the following identities. $$xya\equiv yxa,\quad axy \equiv ayx$$ Without assuming anything further, can we deduce that $X$ satisfies $xy \equiv yx$? In particular, ...