Question

A Euclidean ring possesses a ..... element.

(a) unit. (b) unique
(c) ideal. (d) none​

Answer 1

unity..................

Answer 2

A euclidean ring possesses a (a)unit element.

Definition of Euclidean ring;

A Euclidean ring shows a zero divisors in which an integer norm is associated with division algorithm.

Use of Euclidean ring;

• A Euclidean ring shows the absolute value and the division algorithm representing the quotient and remainder. For example in polynomials norm is the degree.
• In the ring of the integers the Euclidean ring is put through the Euclidean algorithm.
• Every Euclidean domain is the principal that signifies the fundamental theorem of arithmetic.
• So to represent the Euclidean ring R is very necessary for the Euclidean domain.
• Where as the Euclidean ring possesses the unit element.

Hence, for Euclidean ring it signifies the unit element and R which is necessary for Euclidean domain.