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2. Generator (mathematics) - Wikipedia

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

   Generator (mathematics) The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that ...

3. Multiplicative group of integers modulo n - Wikipedia

   en.wikipedia.org/wiki/Multiplicative_group_of...

   Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...

4. Ideal (ring theory) - Wikipedia

   en.wikipedia.org/wiki/Ideal_(ring_theory)

   Ideal (ring theory) In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3.

5. Cyclic group - Wikipedia

   en.wikipedia.org/wiki/Cyclic_group

   A cyclic group is a group which is equal to one of its cyclic subgroups: G = g for some element g, called a generator of G. For a finite cyclic group G of order n we have G = {e, g, g2, ... , gn−1}, where e is the identity element and gi = gj whenever i ≡ j (mod n); in particular gn = g0 = e, and g−1 = gn−1.

6. Field (mathematics) - Wikipedia

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

   e. In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.

7. Multiplication - Wikipedia

   en.wikipedia.org/wiki/Multiplication

   Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit. Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 ⁠ 1 / 2 ⁠ × 2 ⁠ 1 / 2 ⁠ = 11 ⁠ 1 / 4 ⁠