| 41. | The converse does not hold : every right Ore domain is a right Goldie domain, and hence so is every commutative integral domain.
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| 42. | An integral domain is completely integrally closed if and only if the monoid of divisors of " A " is a group.
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| 43. | An element of an integral domain is prime if, and only if, an ideal generated by it is a nonzero prime ideal.
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| 44. | It follows that the unique minimal prime ideal of a reduced and irreducible ring is the zero ideal, so such rings are integral domains.
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| 45. | *PM : polynomial ring over integral domain, id = 6918-- WP guess : polynomial ring over integral domain-- Status:
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| 46. | *PM : polynomial ring over integral domain, id = 6918-- WP guess : polynomial ring over integral domain-- Status:
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| 47. | One would think that integral domains and fields should be given more prominence in the article and should be discussed earlier in and more depth.
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| 48. | If " A " is an integral domain, then " d " is the transcendence degree of its field of fractions.
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| 49. | In general, suppose R is an integral domain and f is a monic univariate polynomial of degree d \ geq 1 with coefficients in R.
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| 50. | A commutative principal ideal ring which is also an integral domain is said to be a " principal ideal domain " ( PID ).
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