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May
4
comment For a polynomial $f\in K[x]$, when is there a constant $c\in K$ such that $f+c$ is irreducible?
Suppose $K=\mathbb{C}$. What are the irreducibles in this case?
Apr
15
comment Subgroups of $ \mathbb{Z}_n$ (integers mod $n$)
Following up on what @quid said, $m$ and $n$ will generate the same subgroup of $\mathbb{Z}_{18}$ if and only if $\gcd(m,18)=\gcd(n,18)$, which you may verify by listing all the cyclic subgroups of $\mathbb{Z}_{18}$. You may restrict each of $m$, $n$ to be in $\mathbb{Z}_{18}$ of course.
Feb
9
comment Non abelian subgroup of a abelian group.
You can have abelian subgroups in a non-abelian group, but not non-abelian subgroups in an abelian group.
Jan
18
comment is complex number under absolute value a group?
Is the number 0 allowed? If so, what is its inverse?
Dec
29
comment Why rationalize the denominator?
@Ahaan - +1 for the answer. Nonetheless, a good teacher, at any level, should have no trouble realizing that your three radical expressions represent the same number. However, having said that, and being a US resident, maybe not.
Dec
29
awarded  Nice Answer
Dec
22
answered Removable discontinuity question
Oct
29
awarded  Yearling
Sep
27
answered Finding a basis for a subspace in $\;\Bbb R^4\;$
Sep
11
comment Cant understand some definitions of abstract algebra, can you help me please?
I don't know the reason for the term "over", but it is used to indicate the field from which the scalars for the scalar multiplication are chosen. In a similar vein, if one talks about the finite dimensional space $F^n$, then one considers this space as being "over $F$" in the sense that the $n$-tuples have entries that come from $F$.
Aug
31
comment A Book for abstract Algebra
I'm currently using Pinter's book in my abstract algebra course because it is well-written, inexpensive, and has great exercise sets that break sometimes difficult discussions into manageable pieces.
Aug
24
comment Does every group have a 'cyclization'?
@Alexander - It certainly seems every group has a trivial one, which is why I don't think the trivial case is very interesting. I'm kind of distracted by other obligations at the moment, but it seems that $\mathbb{Z}$ has both itself and the trivial group as cyclizations.
Aug
24
comment Does every group have a 'cyclization'?
It might make a better question to ask what groups have nontrivial cyclizations, since not all have non-trivial ones.
Aug
24
comment Does every group have a 'cyclization'?
@Bryan - I assumed you wanted a non-trivial cyclization.
Aug
24
answered Does every group have a 'cyclization'?
Aug
2
comment Convergent or divergent $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+1}}\left(\frac{n}{n+1}\right)^n$?
@Nick - One thing to remember with textbook answers is that it is not usually possible, because of space limitiations, to give complete, rigorous answers. So, you get the telegraphic version that says "essentially", i.e., asymptotically, your series is a constant multiple of a divergent series, the harmonic.
Jul
27
comment If one number is thrice the other and their sum is $16$, find the numbers
One number is $x$, the other $3x$. They add to 16, so ... .
Jul
2
awarded  Curious
Jun
30
comment Is Matrix $A^2$ invertible if $A$ is invertible?
Follow Thomas' advice. And what do you know about the inverse of a product of invertible matrices?
Jun
25
comment Is it true that “there is no such thing as the square root of minus one”?
@Andre Nicolas Our mathematical conventions are so economical. Perhaps we subconsciously apply Occam's (or, Ockham's) Razor in making these decisions.