Question

Define th
Q.4.
b. Theory
Unit.​

Answer 1

Answer:

In algebraic number theory, a fundamental unit is a generator (modulo the roots of unity) for the unit group of the ring of integers of a number field, when that group has rank 1 (i.e. when the unit group modulo its torsion subgroup is infinite cyclic). Dirichlet's unit theorem shows that the unit group has rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When the unit group has rank ≥ 1, a basis of it modulo its torsion is called a fundamental system of units.[1] Some authors use the term fundamental unit to mean any element of a fundamental system of units, not restricting to the case of rank 1 (e.g. Neukirch 1999, p. 42).

Answer 2

Explanation:

In ring theory, a unit of a ring is any element that has a multiplicative inverse in: an element such that , where is the multiplicative identity. The set of units of a ring forms a group under multiplication, because is closed under multiplication.