Proper ideal：Ideal (ring theory)
Ideal (ring theory)
Proper Ideal
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Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z.
Proper ideal
https://commalg.subwiki.org
An ideal in a commutative unital ring is termed a proper ideal if it satisfies the following equivalent conditions: The element 1 of the ring, ...
Prime Ideal and Proper Ideal
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A proper ideal is simply an ideal that is different from the whole ring. Share.
代數導論二
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P ⊴ R 是一個proper ideal。若「P P 的一個元素能表為兩個元素相乘時，其中至少有一個會是P P 中的成員」，即：. xy∈P⟺x∈P or y∈P x y ∈ P ⟺ x ∈ P or y ∈ P.
代數導論二Week 2 (Part 1)
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定義：Maximal Ideal. 例子：Z/pZ · 敘述：每個Proper Ideal 都可以找到包住他的Maximal Ideal. 定理：Zorn's Lemma · 敘述：Maximal Ideal = Quotient 之後是個Field.
Ideal (set theory)
https://en.wikipedia.org
In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be small or negligible.
Maximal ideals
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Definition 6.5.9 若R 是一個ring 且M 是R 中的一個nontrivial proper ideal, 如果M 不會包含於R 中其他的nontrivial proper ideal, 則我們稱M 是一個maximal ideal.
abstract algebra
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As you pointed out, use the euclidean algorithm to find a P∈Q[x] so that I=(P). If P is not a constant, then P+1 is not in I. This is ...