integral domain
Quick Summary
An integral domain is a mathematical ring with specific properties. It's a set where you can perform addition and multiplication. For multiplication, it must be commutative (order doesn't matter, so a * b = b * a) and associative (a * (b * c) = (a * b) * c). It also needs a multiplicative identity element (like the number 1) and crucially, it cannot have two different non-zero elements whose product is zero.1
A common example of an integral domain is the set of all integers with standard addition and multiplication. This structure is fundamental in abstract algebra.12
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