Solutions to Irreducible Polynomials & Quotient Rings

In summary, Peter has just finished a post entitled "Linear and Abstract Algebra Forum: Irreducible Polynomials, Quotient Rings, and the Rotman Proposition" on the mathhelpboards.com Linear and Abstract Algebra Forum. He has encountered formatting problems when copying and pasting from other editors, and has changed the "Message Editor Interface: " to the Standard Editor.
  • #1
Math Amateur
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MHB
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I have just finished a post entitled:
[h=1]http://mathhelpboards.com/linear-abstract-algebra-14/irreducible-polynomials-quotient-rings-rotman-proposition-3-116-a-16163.html[/h]on the Linear and Abstract Algebra Forum ...

I want to have the following code recognised:

k(z) \subseteq \text{ I am } \phi

recognised ... BUT when I highlight the text and press sigma, the result is as follows: ?

\(\displaystyle k(z) \subseteq \)\(\displaystyle \text{ I am } \phi\)

Can anyone help me fix this weird problem ...

Peter

 
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  • #2
You have all kinds of formatting tags in the body of your post. Please do yourself a HUGE favor and use the standard editor as opposed to the WYSIWYG editor. When you copy/paste from other editors to the editor here, if you are using the WYSIWYG editor, you will also get, unbeknownst to you, potentially all kinds of formatting codes that will ruin your post. If you are using the standard editor, you will only get the actual text you want when you paste.

The WYSIWYG editor is fine for the casual poster who isn't doing anything sophisticated, but for those more advanced posters, such as yourself, the standard editor is the only way to go. You can change the default editor in your settings.

As a vBulletin coder, I have grown to despise the WYSIWYG editor because it really can make adding editor features problematic and a chore. It is an inline document with innerHTML that must be navigated rather than a simple textarea element that is easily written to and copied from...but I digress. :)
 
  • #3
MarkFL said:
You have all kinds of formatting tags in the body of your post. Please do yourself a HUGE favor and use the standard editor as opposed to the WYSIWYG editor. When you copy/paste from other editors to the editor here, if you are using the WYSIWYG editor, you will also get, unbeknownst to you, potentially all kinds of formatting codes that will ruin your post. If you are using the standard editor, you will only get the actual text you want when you paste.

The WYSIWYG editor is fine for the casual poster who isn't doing anything sophisticated, but for those more advanced posters, such as yourself, the standard editor is the only way to go. You can change the default editor in your settings.

As a vBulletin coder, I have grown to despise the WYSIWYG editor because it really can make adding editor features problematic and a chore. It is an inline document with innerHTML that must be navigated rather than a simple textarea element that is easily written to and copied from...but I digress. :)

Thanks Mark ... appreciate your prompt help ...

I will now go to settings and try to change the editor ...

Peter

- - - Updated - - -

MarkFL said:
You have all kinds of formatting tags in the body of your post. Please do yourself a HUGE favor and use the standard editor as opposed to the WYSIWYG editor. When you copy/paste from other editors to the editor here, if you are using the WYSIWYG editor, you will also get, unbeknownst to you, potentially all kinds of formatting codes that will ruin your post. If you are using the standard editor, you will only get the actual text you want when you paste.

The WYSIWYG editor is fine for the casual poster who isn't doing anything sophisticated, but for those more advanced posters, such as yourself, the standard editor is the only way to go. You can change the default editor in your settings.

As a vBulletin coder, I have grown to despise the WYSIWYG editor because it really can make adding editor features problematic and a chore. It is an inline document with innerHTML that must be navigated rather than a simple textarea element that is easily written to and copied from...but I digress. :)

I have changed the "Message Editor Interface: " to the Standard Editor ... hope that is the right thing to do ...

Peter
 
  • #4
Yes, that should fix your problems. :)
 
  • #5
MarkFL said:
Yes, that should fix your problems. :)

Thanks again, Mark ...
 

FAQ: Solutions to Irreducible Polynomials & Quotient Rings

What is an irreducible polynomial?

An irreducible polynomial is a polynomial that cannot be factored into lower degree polynomials with coefficients in the same field. In other words, it cannot be broken down any further.

How do you determine if a polynomial is irreducible?

To determine if a polynomial is irreducible, you can use the Eisenstein's criterion or the Gauß's lemma. Both methods involve checking if the polynomial satisfies certain conditions, and if it does, then it is irreducible.

What is a quotient ring?

A quotient ring is a type of algebraic structure that is created by "quotienting out" a ring by one of its ideals. This means that we take a ring and "divide" it by a smaller ring inside of it, resulting in a new ring with different properties.

How are irreducible polynomials and quotient rings related?

Irreducible polynomials play a crucial role in the construction and properties of quotient rings. The set of all possible remainders when dividing a polynomial by an irreducible polynomial creates the elements in a quotient ring. Additionally, the quotient ring can be thought of as the "solution space" for the irreducible polynomial.

What are some practical applications of solutions to irreducible polynomials and quotient rings?

Solutions to irreducible polynomials and quotient rings have various applications in fields such as cryptography, coding theory, and signal processing. They are also used in various mathematical proofs and constructions. For example, the construction of finite fields and cyclotomic fields rely on solutions to irreducible polynomials and quotient rings.

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