2d
answered Direct sum of simple modules and Schur's Lemma
2d
comment A finite-dimensional $K$-algebra?
@karparvar I don't know what else there is to say about the definition of $KG$, but I tried to add more to the solution.
2d
comment A finite-dimensional $K$-algebra?
@karparvar OK: I have not seen that particular definition before. What I meant by "dense" is that for every $x\in Q\setminus\{0\}$, there exists $r\in R$ such that $rx\in R\setminus\{0\}$.
2d
revised A finite-dimensional $K$-algebra?
added 247 characters in body
2d
comment A finite-dimensional $K$-algebra?
What definition are you using for an order? I can't recall everything off the top of my head, but doesn't it have to do with the subring being "dense" in the big ring? It's dense in the sense I'm thinking of, but I can't quite interpret your last line.
2d
answered A finite-dimensional $K$-algebra?
2d
comment $M_n(D)$ is left and right-simple?
A ring with identity and only trivial right ideals is a division ring.
Nov
26
comment $\mathbb R^2$ as a plane
What do you want a "plane" to satisfy?
Nov
25
comment Is $\mathbb{C}\bigotimes_\mathbb{R}\mathbb{C}\simeq \mathbb{C}\bigotimes_{\mathbb{C}}\mathbb{C}$?
@Cure No, it's OK to leave this question. It is just another net that will help catch people looking for the same question. But do your best to avoid duplicating questions in the future :) Unavoidable duplication occurs if questions are titled poorly. Eventually we'll collect a sufficient number of titles to deter duplication.
Nov
25
revised Need help determining the pairs of quaternions that anticommute
added 162 characters in body
Nov
25
revised Need help determining the pairs of quaternions that anticommute
added 145 characters in body
Nov
25
comment Is $\mathbb{C}\bigotimes_\mathbb{R}\mathbb{C}\simeq \mathbb{C}\bigotimes_{\mathbb{C}}\mathbb{C}$?
@timbuc you might have better luck doing a google search with "site:math.stackexchange.com" appended
Nov
25
comment Is $\mathbb{C}\bigotimes_\mathbb{R}\mathbb{C}\simeq \mathbb{C}\bigotimes_{\mathbb{C}}\mathbb{C}$?
@john I know what you mean, but actually I rarely have difficulty finding duplicates with the search and/or google. Questions like this are harder though since they've got lots of tex in them. Anyway, I hope you weren't advocating for giving up on duplicate searches before posting questions. It would really be better for posters to have that habit.
Nov
25
comment Concerning Ideals and invertible elements in a commutative ring
@khajvah commutativity is superfluous. A right/left/two sided ideal (of a ring with identity) is the whole ring iff it contains a unit. This proof shows why. Are you not convinced? of course it is healthy to check for sure if it's really not necessary.
Nov
25
comment Prove $\text{rad}(I)/I$ is isomorphic to $\mathfrak{N}(R/I)$
@RicardoCervantes you've got no guarantee the max exists. Anyhow, the two sets are equal pretty much by definition (depending on your definitions.) you probably shouldn't spend time looking for a map.
Nov
25
comment A difficult question on mathematical physics
Hi: FFR, you'll probably attract more attention with a more specific title. Bland titles that could describe a million questions are usually swiftly passed over.
Nov
25
answered Proving the ring $\mathbb{Q}$[$\mathbb{Z}$] is not artinian
Nov
24
comment identify nature of missingness for categorical variables
A perhaps better word for "missingness" is "absence."
Nov
24
comment $I$ is an ideal in $R$ implies that $I[x]$ is an ideal in $R[x]$.
Do you know what the definition of an ideal is? Do you know what $I[x]$ means? If so, the proof nearly writes itself. How about you try to make some progress and edit it into your post?
Nov
24
revised Need help determining the pairs of quaternions that anticommute
added 1 character in body