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2d
comment The coordinate ring of $\varepsilon: xy-1=0$
and also math.stackexchange.com/q/1415542/29335
Feb
2
comment Principal ideal domain with finitely many ideals
Here's the same problem rephrased for UFDs. Maybe not a dupe, but definitely a generalized-dupe.
Feb
2
comment Principal Ideal Domain $R$ and ideal $J\neq 0$ so that that $R/J$ have a finite number of ideals.
Never mind, found a closer duplicate with an answer. Please use the search feature next time.
Feb
2
comment Principal Ideal Domain $R$ and ideal $J\neq 0$ so that that $R/J$ have a finite number of ideals.
No effort duplicate of math.stackexchange.com/q/640403/29335. Unfortunately, those helping that poster only made comments and no solutions. I left a CW answer to rectify the situation. If someone upvotes that then this can be closed as a dupe of that one.
Feb
2
answered Unique factorization domain and principal ideals .
Feb
2
comment Are “$S$-monoids” known to be good for anything?
Hm, what a strange choice to call the set which is acting by the set it is acting upon. It clashes with established terminology like this: $X$ is a $G$-set if it has some action $G\times X\to X$. A more likely name would be something like "$S$ is an (adjective) $M$-monoid." But anyhow, may I ask how you came upon the construction? Just through the context of the 'main example'?
Feb
2
comment Which of the following are true about the ring of continuous real valued functions C[0,1]
d) is false for all sorts of reasons. You should be able to come up with some thoughts on that one.
Feb
2
comment Which of the following are true about the ring of continuous real valued functions C[0,1]
@gautam you ought to try searching for these questions individually. That would definitely get answers for a) and b). It is also just a bad idea in general to post a burst of more than three questions in a single post. Simple is better than complex.
Feb
1
comment How to take the inverse of the matrix $X^{T}X$, when it isn't invertible?
@user136503 The pseudoinverse Alexander is referencing is unique, so no, there should not be 'different results.'
Feb
1
comment How to take the inverse of the matrix $X^{T}X$, when it isn't invertible?
Obviously it is singular even without an algebra package: $X[1,1,1,1,1,1,1,1]^\top=[0,0,0,0,0,0,0,0]^\top$. Then $X$, $X^\top$, and $X^\top X$ are all surely singular. If they think they've found an inverse to $X^\top X$, they are mistaken. That or there is an alternative interpretation that we haven't found.
Feb
1
comment Is the element $(0,0,0)\in\mathbb{R}^3$ a divisor of zero?
Dear @NobleMushtak : I don't even know if "most" is an appropriate qualifier. I'm not sure such clairvoyance is necessary, though. You might really be best off saying "some authors define it this way, and it is clear that your author is one of those." Regards.
Feb
1
comment $\det$ is the only multiplicative nonzero quadratic form on $\mathcal M_2(\Bbb R)$
I have a proof that works if you can prove it for diagonal matrices. Unfortunately, I haven't seen the trick for diagonal matrices, which is a bit disturbing...
Feb
1
answered Prove that the sum of ideals of a ring A equals A and its intersection is zero.
Feb
1
comment Is the element $(0,0,0)\in\mathbb{R}^3$ a divisor of zero?
@CameronWilliams ... depending on author, of course, and yes, obviously in this person's course :)
Feb
1
comment Is the element $(0,0,0)\in\mathbb{R}^3$ a divisor of zero?
The very link you include subscribes to the definition that allows zero to be a zero divisor. It is probably not the case that "mathematicians prefer" the restricted definition, although some particular specialization might.
Jan
30
comment can every object be represented mathematically?
The first question is impossibly vague, but the second question makes me think your real question is "how can I develop equation all descriptions of some pictures I have in mind?" which is a better question. You might want to rewrite to emphasize that.
Jan
30
comment What is so special about the Schwarz Inequality?
You don't find it interesting that the inner product of two vectors is limited by the product of the two norms?
Jan
30
comment I don't know Maschke's theorem in the group representation.
An action $G\times V\to V$ should correspond with a module action $F[G]\times V\to V$
Jan
29
comment Is there a domain which is not UFD but has a maximal principal ideal?
And in case anyone reads later, $(p,X)=(p)$
Jan
29
comment Is there a domain which is not UFD but has a maximal principal ideal?
OK, so just proof by exhaustive description. Thanks