← MATH 01340 · Modern Algebra I
MATH 01340 · Rings & fields (intro)
Integral domains / fields
Definition
Integral domain: commutative ring with 1, no zero divisors (ab=0 ⇒ a=0 or b=0). Field: commutative ring with 1 where every nonzero element is a unit (e.g. ℚ, ℝ, ℂ, ℤₚ).
Read this
Finite integral domains are fields. ℤ is a domain but not a field.
ℤₙ is a field iff n is prime.
Fields support the algebra you use in linear algebra over F.
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Try this
Attempt each problem first, then open the worked solution.
1.Explain why ℤ₄ is not an integral domain.