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Mathematics Questions ∷ Beginners and Expert Mathematics Questions

Does $f otimes A 1 {A/m}:M otimes A/m to N otimes A/m$ injective for all maximal $m$ imply $f$ is an isomorphism? Let $A$ be a commutative ring. Suppose $f colon M to N$ is a morphism of free $A$-modules of equal, finite rank. If $f otimes A 1 {A/m}$ is injective for all maximal ideals of $A$, does this imply $f$ . Inequality involving $x$, $x 3$,$ sin(x), cos(x)$. Can the interior of a manifold be orientable but not its boundary? Making sense of multiplication in tensor product. Assume that $X'X$ is pos...

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Mathematics Questions ∷ Beginners and Expert Mathematics Questions | math.troplet.com Reviews
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Does $f otimes A 1 {A/m}:M otimes A/m to N otimes A/m$ injective for all maximal $m$ imply $f$ is an isomorphism? Let $A$ be a commutative ring. Suppose $f colon M to N$ is a morphism of free $A$-modules of equal, finite rank. If $f otimes A 1 {A/m}$ is injective for all maximal ideals of $A$, does this imply $f$ . Inequality involving $x$, $x 3$,$ sin(x), cos(x)$. Can the interior of a manifold be orientable but not its boundary? Making sense of multiplication in tensor product. Assume that $X'X$ is pos...
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Mathematics Questions ∷ Beginners and Expert Mathematics Questions | math.troplet.com Reviews

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Does $f otimes A 1 {A/m}:M otimes A/m to N otimes A/m$ injective for all maximal $m$ imply $f$ is an isomorphism? Let $A$ be a commutative ring. Suppose $f colon M to N$ is a morphism of free $A$-modules of equal, finite rank. If $f otimes A 1 {A/m}$ is injective for all maximal ideals of $A$, does this imply $f$ . Inequality involving $x$, $x 3$,$ sin(x), cos(x)$. Can the interior of a manifold be orientable but not its boundary? Making sense of multiplication in tensor product. Assume that $X'X$ is pos...

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Featured Questions - Part 1 ∷ Mathematics Questions

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Sheaf cohomology on projective space. In defining a cohomology theory on sheaves of projective spaces, we define $ mathscr{S} {[k]} = prod { left J right = k 1} mathscr{S} J.$ So essentially, we take the product of the $ mathscr{S}. Upper bound for p-norm of pre-frame operator $U$. Let $ mathcal H$ be a Hilbert space and $ { f i } {i=1} infty$ a frame for $ mathcal H$ with bounds $A$ and $B$. Define the operator $ U: ell p( mathbb N) to mathcal H, U {c i }:= sum {i=1} . Counting to $P$ game - strategy?

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[SOLVED] Can the interior of a manifold be orientable but not its boundary? ∷ Mathematics Questions

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Can the interior of a manifold be orientable but not its boundary? August 18th, 2015 2:27:51. 13; . Suppose $M m$ is a manifold with boundary. If we are given an orientation for $M$, we can then derive an orientation for $ partial M$ by considering the orientation of $TM$ at $ partial M$ and then using an outward-pointing vector to get an orientation of $T( partial M)$. This made me wonder: is it possible that $M circ = M setminus partial M$ is orientable but $M$ is not? August 18th, 2015 2:42:59. The A...

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[SOLVED] inequality involving $x$, $x^3$,$\sin(x),\cos(x)$ ∷ Mathematics Questions

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Inequality involving $x$, $x 3$,$ sin(x), cos(x)$. August 18th, 2015 2:29:10. 13; . Let $x in left[0, dfrac { pi} 2 right]$. Prove the inequality. 6x ge 6 sin x x 3 cdot cos x$. There is nice solution using Taylor expansion. Is there other one? EDIT) Let $f(x) = 6 x - 6 sin(x) - x 3 cos(x)$. $f' (x) = 6 ( sin(x) - x cos(x) 6 x 2 sin(x) x 3 cos(x)$. But $f(0)=0$ and $f'(0) = 0$, so $ f(x) = f(0) f'(0) x int 0 x (x-t) f' (t) ; dt ge 0$ for $0 le x le pi/2$. August 18th, 2015 2:52:39.

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[ASK] Is there any example of a Category without generators? ∷ Mathematics Questions

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Is there any example of a Category without generators? August 18th, 2015 1:41:41. 13; . I was looking of an example of a category (a non trivial example) without generators (seperators). Is there any nice example? Or every category that we are using has generators? The property of admitting a small family of generators implies and is closely related to the property that a category is concretizable. August 18th, 2015 4:47:38. For why), so $ mathrm{Grp} { mathrm{op} $ can't have a generating set.

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Most Voted Questions - Part 1 ∷ Mathematics Questions

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Can I use my powers for good? I hesitate to ask this question, but I read a lot of the career advice from MathOverflow and math.stackexchange, and I couldn't find anything similar. Four years after the PhD, I am pretty sure that . How long will it take Marie to saw another board into 3 pieces? So this is supposed to be really simple, and it's taken from the following picture: Text-only: It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will . Here's my problem...

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Mathematics Questions ∷ Beginners and Expert Mathematics Questions

Does $f otimes A 1 {A/m}:M otimes A/m to N otimes A/m$ injective for all maximal $m$ imply $f$ is an isomorphism? Let $A$ be a commutative ring. Suppose $f colon M to N$ is a morphism of free $A$-modules of equal, finite rank. If $f otimes A 1 {A/m}$ is injective for all maximal ideals of $A$, does this imply $f$ . Inequality involving $x$, $x 3$,$ sin(x), cos(x)$. Can the interior of a manifold be orientable but not its boundary? Making sense of multiplication in tensor product. Assume that $X'X$ is pos...

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