# Medial: Quiz

Question 1: In ________, a medial magma (or medial groupoid) is a set with a binary operation which satisfies the identity
Abstract algebraGroup (mathematics)Vector spaceNumber theory

Question 2: This can easily be expressed in terms of a commutative diagram, and thus leads to the notion of a medial magma object in a category with a ________.
Binary relationCartesian productCardinal numberDirect product

Question 3: An ________ is an entropic algebra if every two operations satisfy a generalization of the medial identity.
Algebraic structureGroup (mathematics)Vector spaceRing (mathematics)

Question 4: Any ________ semigroup is a medial magma, and a medial magma has an identity element if and only if it is a commutative monoid.
CommutativityRing (mathematics)Vector spaceGroup (mathematics)

Question 5: A magma M is medial if and only if its binary operation is a homomorphism from the ________ M x M to M.
Binary relationCartesian productDirect productCardinal number

Question 6: An elementary example of a nonassociative medial quasigroup can be constructed as follows: take an ________ except the group of order 2 (written additively) and define a new operation by x * y = (− x) + (− y).
Group (mathematics)Group homomorphismAbelian groupSimple group