Dec
13
answered Ring whose all ideals are double-sided is commutative?
Dec
13
comment Why are every structures I study based on Real number?
@TaxxiDriver Yes, it's just "the nicest" field to have when working with vectors using geometric intuition.
Dec
13
revised Why are every structures I study based on Real number?
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Dec
13
revised Why are every structures I study based on Real number?
added 250 characters in body
Dec
13
answered Why are every structures I study based on Real number?
Dec
13
comment Definition of division algebra
@learner I don't see "is a ring without nonzero zero divisors" anywhere, so NO, I do not see any definition of "domain" there.
Dec
13
comment Definition of division algebra
An associative division algebra will certainly not have zero divisors. An associative ring without zero divisors is called a domain. There are domains that aren't division algebras, and there are division algebras which aren't associative and aren't domains.
Dec
12
answered Semisimplicity of the ring $\mathbb Z_n$
Dec
12
answered Intuition for why finite integral domain is a field
Dec
12
answered Looking for example of a commutative non-unital ring in which every maximal ideal is a prime ideal
Dec
12
comment Looking for example of a commutative non-unital ring in which every maximal ideal is a prime ideal
@Souvik Thanks for adding more context. That's enough (for me anyhow) to take the question seriously. I hope you'll apply similar effort to future questions :)
Dec
12
comment How do $\Bbb{R}$ and $\Bbb{R}^2$ have the same dimension over $\Bbb{Q}$ as vector spaces?
@algebraically_speaking For infinite bases, wouldn't you agree that "same dimension" should mean "have bases of the same cardinality"?
Dec
12
revised Determine which roots of unity have degree at most 3
edited tags; edited title
Dec
12
comment Determine which roots of unity have degree at most 3
@wu Have you heard of roots of unity? Do you know the relationship of the degree of extensions to minimal polynomials?
Dec
12
comment Looking for example of a commutative non-unital ring in which every maximal ideal is a prime ideal
@PrzemysławScherwentke Recently people started noticing that the user's questions are very often problem statements in the imperative with no effort involved, so this is the natural progression in a case like this. S/He's been asked at least once recently to not do this, so it is a little disappointing to see it continue...
Dec
11
comment What is the name of this curve?
You also might be interested in a tractrix (which is not the same thing)
Dec
11
comment What to mathematics books to read?
Could anybody really even survive a full reading of the 20 greatest math books ever written?
Dec
11
comment Linear Algebra--searching a name for certain transformations
What is the proper english name "rotation matrix"
Dec
11
answered What exactly is the 'tension' between arithmetic and geometry?
Dec
11
answered Proving elementary property about hyperplanes.