Trailer for my "ideal" Season 7 - No potential slayers, no Caleb, No Principal Wood, more limited Spike and Andrew screentime. Just the core Scoobies v.s the Hellmouth one last time and each with their own season-long individual arcs. v.redd.it/l2lpqydh2gl61
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👤︎ u/GreyStagg
📅︎ Mar 06 2021
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Cual es tu trabajo ideal, siendo trabajar la satisfacción principal?

Cual seria tu trabajo ideal, ganas lo suficiente para vivir normal, nada de lujos, no hay fama, no hay aumento y siendo la labor la satisfacción principal

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👤︎ u/daardoo
📅︎ Apr 06 2021
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PURE: Principal Ideal Domains

Hey! I have this question (please click the link to see it, reddit crops half of it off) here that I’m stuck on.

So far, I’ve divided the two polynomials and got the answer as (x-1) + 2/(x+1) but I’m not sure where to go from here.

Any help is really appreciated, thank you :)

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👤︎ u/Sazzo100
📅︎ Feb 08 2021
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Let R be an Integral domain and also a principal ideals ring, proof that every pair of non-zero elements of R has a LCM and a GCD

Also calculate in the ring Z[i] the lcm and gcd of 14+2i and 21+26i

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📅︎ Mar 12 2021
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In America, the founding principals are constantly talked about and debated endlessly (first & second amendment). In the rest of the world, what are the founding principals or ideals that 100s of years later are still being discussed and fought over?
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📅︎ Jul 28 2020
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Norm of a principal ideal=field norm of generator

This is a property which can be easily seen for the ring of integers of low degree fields, but for higher degree fields this turns into what I see as the least obvious equality of all time. This basically says that the product of the roots of the minimal polynomial of the ideal generator is equal to the determinant of the map sending the ring onto the ideal. Another way to kinda rephrase this is how does the determinant relate to the roots of a polynomial?

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📅︎ Jan 29 2020
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Why is no principal ideal in Z[x] maximal?

Let I = ( f (x) ) be a principal ideal in Z [ x ] . I understand that if f(x) = a , a constant, then the ideal ( a , x ) contains ( a ) , so ( a ) is not maximal. However, consider the case where f(x) has positive degree. A source I found online said to consider a prime p not dividing the leading term of f(x) . Then the ideal (p, f(x) ) contains ( f(x) ) . Why do we need to consider p not dividing the leading term of f(x) ? Source here: https://math.stackexchange.com/questions/2120064/why-principal-ideals-in-zx-are-not-maximal

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📅︎ Feb 11 2018
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Spinnet - Principal Ideal [Literature Recordings] youtube.com/watch?v=XckD_…
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📅︎ Oct 20 2018
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God is dead: St Stephen's Principal fails to be humbled by ideals greater than himself catchnews.com/life-societ…
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📅︎ Feb 13 2016
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[Abstract Algebra] If (r) denotes the principal ideal generated by r and R is unitary and commutative, must (r)+(s) = (r+s)?

If not, in what circumstance does it and why? Also, the containment from the right to the left follows directly from distributivity, right?

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👤︎ u/reeve512
📅︎ Dec 05 2011
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[Abstract Algebra] Prove that the ideal <2,1+√(-5)> is not principal in Z[√(-5)].

The title says it all: I need assistance proving that the ideal <2,1+√(-5)> is not principal in Z[√(-5)].

I've started off by supposing that it is principal and generated by x+y√(-5). Then, there exist A=a+a'√(-5) and B=b+b'√(-5) in Z[√(-5)] such that

2 = A(x+y√(-5)) and 1+√(-5) = B(x+y√(-5)).

I've played around with expanding the terms and rearranging them, but I can't see anything that forces a contradiction. Can anyone point me in the right direction? All help is greatly appreciated. Thanks.

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📅︎ Nov 29 2012
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Which principal ideals of Z[x] are maximal?

I am still fairly new to Ring theory, so I could use a little direction on this one. I'd rather just get advice than the complete solution, as I feel like this shouldn't be too difficult.

Here Z[x] is the ring of polynomials over the integers.

I think I understand the proof that the maximal ideals of Z[x] are generated by an irreducible polynomial and a prime, but I am having trouble determining which, if any, of these are principal ideals.

Other than the trivial case, how should I be looking at this? I was thinking that ideals generated by an irreducible polynomial whose coefficients are relatively prime might work, but of course (x) is not maximal, for example.

Any suggestions?

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📅︎ Feb 23 2012
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The Wizardly Ways of a Tech Lab - "In the ideal science lab, research is the principal driving force...In the (MIT) Media Lab, by contrast, the overriding concern is the development of a device, a machine, a process, a system." online.wsj.com/article/SB…
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📅︎ Jun 11 2011
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Cual es tu trabajo ideal, siendo trabajar la satisfacción principal?

Cual seria tu trabajo ideal, ganas lo suficiente para vivir normal, nada de lujos, no hay fama, no hay aumento y siendo la labor la satisfacción principal

👍︎ 5
💬︎
👤︎ u/daardoo
📅︎ Apr 06 2021
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Why are no principal ideals in Z[x] maximal?

Let I = ( f (x) ) be a principal ideal in Z [ x ] . I understand that if f(x) = a , a constant, then the ideal ( a , x ) contains ( a ) , so ( a ) is not maximal. However, consider the case where f(x) has positive degree. A source I found online said to consider a prime p not dividing the leading term of f(x) . Then the ideal (p, f(x) ) contains ( f(x) ) . Why do we need to consider p not dividing the leading term of f(x) ? Source here: https://math.stackexchange.com/questions/2120064/why-principal-ideals-in-zx-are-not-maximal[1]

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📅︎ Feb 11 2018
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Abstract Algebra (Principal Ideal Ring)

A principal ideal ring is a ring with the property that every ideal has the form <a>. Show that the homomorphic image of a principal ideal ring is a principal ideal ring.

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👤︎ u/Yogi_Bare
📅︎ Oct 21 2015
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