To write twelve more than the quotient of three and the number is nine in numbers, it is the math equation 12+ (x/3)=9. AnswerParty on.
In algebra, which is a broad division of mathematics, abstract algebra is a common name for the sub-area that studies algebraic structures in their own right. Such structures include groups, rings, fields, modules, vector spaces, and algebras. The specific term abstract algebra was coined at the beginning of the 20th century to distinguish this area from the other parts of algebra. The term modern algebra has also been used to denote abstract algebra.
Two mathematical subject areas that study the properties of algebraic structures viewed as a whole are universal algebra and category theory. Algebraic structures, together with the associated homomorphisms, form categories. Category theory is a powerful formalism for studying and comparing different algebraic structures.
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring or residue class ring, is a construction quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two-sided ideal I in R, and constructs a new ring, the quotient ring R/I, essentially by requiring that all elements of I be zero in R. Intuitively, the quotient ring R/I is a "simplified version" of R where the elements of I are "ignored".
Quotient rings are distinct from the so-called 'quotient field', or field of fractions, of an integral domain as well as from the more general 'rings of quotients' obtained by localization.