Carat (mass) Despite its being a non-metric unit, a number of metric countries have used this unit for its limited range of application. The Board of Trade carat was divisible into four "diamond grains", but measurements were typically made in multiples of carat. There were also two varieties of "refiners' carats" once used in the United Kingdom — the pound carat and the ounce carat. The pound troy was divisible into 24 "pound carats" of 240 grains troy each; the pound carat was divisible into four "pound grains" of 60 grains troy each; and the pound grain was divisible into four "pound
Pure subgroup While pure projective modules have not found as many applications as pure injectives, they are more closely related to the original work: A module is pure projective if it is a direct summand of a direct sum of finitely presented modules. In the case of the integers and Abelian groups a pure projective module amounts to a direct sum of cyclic groups. Pure subgroup In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas. A