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The preimage of a prime ideal under a ring homomorphism is a prime ideal. The analogous fact is not always true for maximal ideals, which is one reason algebraic geometers define the spectrum of a ring to be its set of prime rather than maximal ideals; one wants a homomorphism of rings to give a map between their spectra.
We define a matching to be maximal ( as opposed to maximum) if it is not a proper subset. of any other matching ( i. e. a matching that cannot be enlarged by including more edges) . Show that. in any graph, the size of any maximal matching M is at least half the size of a maximum matching. Also, give an example where it is exactly one - half.
Example 16.36 16.36. Let pZ p Z be an ideal in Z, Z, where p p is prime. Solution. Then pZ p Z is a maximal ideal since Z/pZ ≅ Zp Z / p Z ≅ Z p is a field. A proper ideal P P in a commutative ring R R is called a prime ideal if whenever ab ∈ P, a b ∈ P, then either a ∈ P a ∈ P or b ∈ P. b ∈ P. 6. It is possible to define prime ...
Define the minimum percentage and/or number of variant reads in a background of normal reads required to call a variant ‘detected’ at your established level of confidence and sensitivity. Define maximal allowable strand bias (if applicable).
Antichain. In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable . The size of the largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered ...
Jan 20, 2016 · It is well known that the Hardy-Littlewood maximal function plays an important role in many parts of analysis. It is a classical mean operator, and it is frequently used to majorize other important operators in harmonic analysis. It is clear that. $$ M^ {c}f (x)\le Mf (x)\le2^ {n} M^ {c}f (x) $$. holds for all \ (x\in\Bbb {R}^ {n}\).
maximal翻譯：最大的;最高的。了解更多。
