Mary of Teck's son abdicated the throne in 1902.
In abstract algebra , a medial magma , or medial groupoid , is a set with a binary operation which satisfies the identity. abstract algebra. abstract algebra. binary operation. binary operation. identity. identity ( mathematics ). magma. magma ( algebra ). groupoid. groupoid. , or more simply ,. using the convention that juxtaposition denotes the same operation but has higher precedence .. A magma or groupoid is an algebraic structure that generalizes a group .. magma. magma ( algebra ). groupoid. groupoid. This identity has been variously called medial , abelian , alternation , transposition , interchange , bi-commutative , bisymmetric , surcommutative , entropic etc. .. identity. identity ( mathematics ). commutative. commutative. Any commutative semigroup is a medial magma , and a medial magma has an identity element if and only if it is a commutative monoid .. identity. identity ( mathematics ). magma. magma ( algebra ). commutative. commutative. semigroup. semigroup. identity element. identity element. monoid. monoid. Another class of semigroups forming medial magmas are the normal bands .. normal bands. Band ( mathematics ). Medial magmas need not be associative  : for any nontrivial abelian group and integers , replacing the group operation with the binary operation yields a medial magma which in general is neither associative nor commutative .. binary operation. binary operation. magma. magma ( algebra ). commutative. commutative. abelian group. abelian group. Using the categorial definition of the product , one may define the Cartesian square magma with the operation. magma. magma ( algebra ). categorial. category theory. product. product ( category theory ). Cartesian square. Cartesian square. The binary operation of , considered as a function on , maps to , to , and to .. binary operation. binary operation. Hence , a magma is medial if and only if its binary operation is a magma homomorphism from to .. binary operation. binary operation. magma. magma ( algebra ). homomorphism. homomorphism. 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 Cartesian product .. magma. magma ( algebra ). commutative. commutative. product. product ( category theory ). commutative diagram. commutative diagram. category with a Cartesian product. Cartesian closed category. -LRB- See the discussion in auto magma object . -RRB-. magma. magma ( algebra ). auto magma object. auto magma object. If and are endomorphisms of a medial magma , then the mapping defined by pointwise multiplication. magma. magma ( algebra ). is itself an endomorphism .. endomorphism. endomorphism