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2. Graded ring - Wikipedia

   en.wikipedia.org/wiki/Graded_ring

   Example: Given an ideal I in a commutative ring R and an R-module M, the direct sum = / + is a graded module over the associated graded ring / +. A morphism f : N → M {\displaystyle f:N\to M} of graded modules, called a graded morphism or graded homomorphism , is a homomorphism of the underlying modules that respects grading; i.e., ⁠ f ( N ...

3. Quotient - Wikipedia

   en.wikipedia.org/wiki/Quotient

   In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈkwoʊʃənt /) is a quantity produced by the division of two numbers. [ 1] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) [ 2] or a fraction or ratio (in the ...

4. Division (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Division_(mathematics)

   Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...

5. Rational number - Wikipedia

   en.wikipedia.org/wiki/Rational_number

   In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠ ⁠ of two integers, a numerator p and a non-zero denominator q. [ 1] For example, ⁠ ⁠ is a rational number, as is every integer (e.g., ). The set of all rational numbers, also referred to as " the rationals ", [ 2] the field of rationals[ 3 ...

6. Chunking (division) - Wikipedia

   en.wikipedia.org/wiki/Chunking_(division)

   Chunking (division) In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial ...

7. Ring (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Ring_(mathematics)

   Definition. A ring is a set R equipped with two binary operations [ a] + (addition) and ⋅ (multiplication) satisfying the following three sets of axioms, called the ring axioms: [ 1][ 2][ 3] R is an abelian group under addition, meaning that: (a + b) + c = a + (b + c) for all a, b, c in R (that is, + is associative ).