International Standard Music Number 3 left to right. These weighted digits are added together. The check digit is the integer between 0 and 9 that makes the sum a multiple of 10. For instance, for the item with ISMN beginning 979-0-060-11561: As 85 mod 10 = 5, the check digit is 10 - 5 = 5 and the full number is 979-0-060-11561-5. For another example, Robert Fripp's collection of Guitar Craft scores has the ISMN 979-0-9016791-7-7. Given first 12 digits 979-0-9016791-7, the ISMN algorithm evaluates which implies that the check digit is indeed 7 (because 123+7=130=13x10). International Standard Music Number The International Standard Music
Opposite group Opposite group In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. Monoids, groups, rings, and algebras can be viewed as categories with a single object. The construction of the opposite category generalizes the opposite group, opposite ring, etc. Let formula_1 be a group under the operation formula_2. The opposite group of formula_1, denoted formula_4, has the same underlying set as formula_1, and its group operation formula_6 is defined by formula_7. If formula_1 is abelian, then