An Integral Domain is a type of mathematical structure that consists of a set of elements, operations, and properties that follow certain rules. It is a generalization of the concept of a field, where the division operation is not always defined for all elements.
When a^2 = 1 in an Integral Domain, it means that the element "a" is its own inverse. In other words, when "a" is multiplied by itself, the result is equal to the multiplicative identity element, which is 1.
No, in an Integral Domain, an element can only have one square root. This is because the property a^2 = 1 implies that the element "a" is its own inverse, and there can only be one inverse for any given element.
An Integral Domain is a generalization of a Field, where the only difference is that the division operation is not defined for all elements in an Integral Domain. In a Field, every non-zero element has a defined inverse for both multiplication and addition.
Yes, every Integral Domain is also a Commutative Ring. This is because an Integral Domain satisfies all the properties of a Commutative Ring, such as closure, associativity, commutativity, and distributivity.