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An ideal P of a commutative ring R is prime if it satisfies two properties: first, if the product ab of two elements a and b in R is in P, then at least one of a or b must be in P; second, P is not the entire ring R.
Conditions: R is a commutative ring.; P is an ideal of R.; For all a, b in R, if ab is in P, then a is in P or b is in P.; P is not equal to R.
2:08 – 2:25Watch this moment ↗
An ideal P of a commutative ring R is prime if it satisfies two properties: first, if the product ab of two elements a and b in R is in P, then at least one of a or b must be in P; second, P is not the entire ring R.
Conditions: R is a commutative ring.; P is an ideal of R.; For all a, b in R, if ab is in P, then a is in P or b is in P.; P is not equal to R.
2:08 – 2:25Watch this moment ↗