Abstract algebraGeneralizing numbersGroupsRingsGeneralizing vectorsInner products of vectorsNorms and angles of vectorsMultilinear forms on vectorsOrthogonality of vectorsAlgebras: multiplication of vectorsDivision algebrasCombining algebraic objectsThe direct product and direct sumThe free productThe tensor productDividing algebraic objectsQuotient groupsSemidirect productsQuotient ringsRelated constructions and factsSummaryPreviousNext