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Jun
23
comment Dual of Osofsky Theorem
@karparvar I could not find a dual replacement of $E(N)$... Do you mean that the projective cover was not suitable? You would get projective covers if you assumed the ring was right perfect. Other than that, all you have is the flat cover.
Jun
23
answered Pathologies in “rng”
Jun
23
comment Please give an example of a ring that does NOT have a multiplicative identity but contains a subring that does have an identity..
I cannot think of an example of a ring without an identity Any nontrivial ideal of a domain (ring without nonzero zero divisors) is an example, as is any nonzero nil ideal of a ring (an ideal whose elements are nilpotent.)
Jun
23
comment All simple modules are projective $\Rightarrow$ semisimple
The way I did it at the dupe is to observe there are no essential maximal right ideals, and this means all right ideals are direct summands.
Jun
20
comment Monoid as a single object category
A footnote to another solution should, well, be a footnote on that solution (or rather a comment or two.)
Jun
20
revised Reflections in Euclidean plane
deleted 158 characters in body
Jun
20
answered Reflections in Euclidean plane
Jun
20
comment Determine all maximal and prime ideals of the polynomial ring $\Bbb C[x]$
@permute the last sentence is a little ambiguous. You probably want to make it clear that you know the zero ideal isn't maximal.
Jun
19
comment Why is the observation that proof of the Fundamental Theorem of Algebra requires some topology not tautological?
@TorsionSquid What exactly do you mean by "only needs the algebraic numbers"? I'm just not sure, so I'd appreciate the clarification.
Jun
19
comment Why is the observation that proof of the Fundamental Theorem of Algebra requires some topology not tautological?
Dear @BalarkaSen : I dunno: one can argue fairly strongly by saying that the LUB axiom amounts to the topological completeness of the real numbers. This "no gaps" property is pretty solidly topological... Many parts of elementary analysis are purely topological, so I'm not sure where to draw the line. Regards
Jun
19
comment What will the recursion tree of Fibonacci series look like?
@MaksimDmitriev I had hoped you would read the post and click either of the fixed links, but I guess I didn't bother moving the original link. I did this also, and now you can't go wrong. Regards.
Jun
19
revised What will the recursion tree of Fibonacci series look like?
added 43 characters in body
Jun
18
answered Very elementary question on isosceles triangles, Geometry
Jun
18
comment If $H$ and $K$ are solvable subgroups of G with $H$ normal in $G$, then $HK$ is a solvable subgroup of $G$
If this problem is true, then your question is a false one. Replacing $G$ with $HK$, you'd get a counterexample to this question. Where did you find the problem?
Jun
18
comment What will the recursion tree of Fibonacci series look like?
@MaksimDmitriev Done.
Jun
18
revised What will the recursion tree of Fibonacci series look like?
added 657 characters in body
Jun
18
comment Modules over a monoid: trouble with the definition.
I was going to say that it is just a writing convention to simplify writing the action, but Zev has beaten me to it. There is no pre-existing operation.
Jun
18
comment Riemannian geometry vs Hyperbolic geometry
This reminds me of a question I once asked about hyperbolic geometry and spaces with indefinite metric signature which you may find useful.
Jun
15
answered Is the zero ring a domain?
Jun
15
comment Algebra. If $R$ is a commutative associative ring with neutral element.
@MattSamuel : I agree with Bill in this case. Prime ideals are explicitly defined to be proper ideals of $R$ in every text I know (which is a lot), no exceptions. Allowing the entire ring to be a prime ideal does not "fit" into the big scheme well. However, $R$ is allowed to be a semiprime ideal in the same texts.