20h
comment Under what operation prime numbers form a group?
@JyrkiLahtonen Transport of structure is the term I'm familiar with.
Mar
22
comment Is the following set connected given that the union and intersection is connected
How do you know that $S_1 \cap U_2$ and $S_2 \cap U_2$ are non-empty?
Mar
22
answered Is the following set connected given that the union and intersection is connected
Mar
20
comment Finding an isomorphism between rings
@algebar87 This follows from the polynomial division algorithm. Each member of $\mathbb F_3[x] / (x^2 + 1)$ can be uniquely represented by a polynomial of degree at most $1$. I'm sure you've come across this idea as you study fields. What book are you following?
Mar
19
comment Finding an isomorphism between rings
All we know is that $(a + bx)^2 + (a + bx) + 2 \in (x^2 + 1)$. We need a polynomial of degree one plus a multiple of $x^2 + 1$ before we can assume that coefficients are zero.
Mar
19
answered Finding an isomorphism between rings
Mar
19
comment Non-Noetherian ring with Noetherian quotient
Exactly. Use $\{0\}$. I think $I$ is mentioned just to tell you that $R$ is not Noetherian.
Mar
19
comment Non-Noetherian ring with Noetherian quotient
The existence of a maximal ideal in any commutative ring with $1$ is given by Zorn's lemma. Any reason why you cannot use that?
Mar
19
revised How to use variables in SQL statement in Python?
Fix comma splice
Mar
15
comment Let D be a principal ideal domain. Prove that every prime ideal in D is a maximal ideal in D.
@TheEmperorofIceCream Principal ideal domain usually implies that the ring is commutative.
Mar
15
comment Let D be a principal ideal domain. Prove that every prime ideal in D is a maximal ideal in D.
If $(x) \subset (y)$, then $x$ is a member of $(y)$. Hence $x = ay$ for some $a$.
Mar
15
answered Let D be a principal ideal domain. Prove that every prime ideal in D is a maximal ideal in D.
Mar
8
comment Examples of Separable Spaces that are not Second-Countable
The Sorgenfrey line.
Mar
6
awarded Good Answer
Feb
27
comment degree of a map $f:S^1\rightarrow S^1$
See this question. More generally, see proposition 2B.6 in Hatcher's Algebraic Topology. This is usually used to prove Borsuk-Ulam.
Feb
25
comment Ring of quotients: find number of elements in $Q(\mathbb{Z}_4,\{1,3\})$
Alternatively, just note that $3$ is already a unit in $\mathbb Z_4$...
Feb
25
comment Ring of quotients: find number of elements in $Q(\mathbb{Z}_4,\{1,3\})$
My guess is that you want $S^{-1}R$ for $R = \mathbb Z_4$ and $S = \{1, 3\}$. You already have the direct product $R \times S$. Try to find the required equivalence classes.
Feb
23
awarded Populist
Feb
23
comment Proving a certain inequality
Why is this tagged as [tag:general-topology]?
Feb
23
awarded Nice Answer
1 2 3 4 5