Integral Domain

Integral Domain is a #Ring which satisfies the following properties including those in #Group, #Abelian Group and #Communicative Ring.

Multiplicative identity, where \(\exist x \in S, \forall a \in S, ax = xa = a\).
No zero divisors, where if \(a, b \in S\) and \(ab = 0\), then either \(a = 0\) or \(b = 0\).

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Ring

If the multiplicative operation has an identity and no zero divisors, it forms Integral Domain#.
Field

Field is a Set# \(S\), together with two operations \(+\) and \(*\), which has the following properties including those in #Group, #Abelian Group, #Ring, #Communicative Ring, and #Integral Domain:
Algebraic Structure

Integral Domain#