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 Yearling
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  • 0 posts edited
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  • 14 votes cast
Apr
12
comment Some commutator identities
Are $x$, $y$ and $z$ arbitrary? Then letting $x = e$ in the first commutator yields $y = e$.In a similar fashion we will have $z = e$ from the second and and $x = e$ from the third.
Mar
20
comment Divisibility by 4 (induction proof)
$n^{4} - n^{2} = n^{2} (n + 1) (n - 1)$ so you don't have to resort to induction to prove that it is divisible by $3$ and $4$ (for $n \in \mathbb{N}, n \geq 2$): one of $n - 1$, $n$,$n + 1$ must be a multiple of $3$ since they are consecutive integers. If $n$ is odd, then $n - 1$ and $n + 1$ are even. if $n$ is even then $n^{2}$ is divisible by $4$.
Mar
18
comment Ideal proof in a ring R
@fudges: Well I overlooked the possibility that $R$ is a rng, not a ring.
Mar
18
comment Ideal proof in a ring R
In this case, the definition does look redundant, but the general colon ideal is defined as $I \colon J = \lbrace r \in R \mid r J \subset I \rbrace$ for ideals $I, J \subset R$.
Mar
18
comment Ideal proof in a ring R
I guess $K$ is the colon ideal $I \colon R$.which is equal to $I$.
Mar
16
comment “This statement is false” - Propositional Logic
I don't know if the statement conforms to an $n$-ary logic for some suitable $n \geq 3$ (I am sceptical if there exists such an $n$, though.) I would reply to your instructor that we cannot create a truth table since we cannot decide the truth value for that statement.
Mar
16
comment “This statement is false” - Propositional Logic
It means that it does not conform to the binary logic.
Mar
16
revised “This statement is false” - Propositional Logic
added 269 characters in body
Mar
16
answered “This statement is false” - Propositional Logic
Mar
14
comment Good textbooks on homological algebra
Thanks! I browsed Gelfand and Manin. it looks very good (but a bit marred by the remaining typos that escaped revision.) --- accepted ---
Mar
14
accepted Good textbooks on homological algebra
Mar
14
comment Good textbooks on homological algebra
Thanks! My impression is Weibel is a good book except the first chapter which is too sketchy. (Of course I would not care if the book were not titled "introduction". ) --- upvoted ---
Mar
13
comment Good textbooks on homological algebra
@Watson: The question looks duplicate, but (luckily for me) the answers do not. In fact the answers I got are more suited to my concern 1) through 4) above than the ones posted in math.stackexchange.com/questions/28646/….
Mar
13
revised Good textbooks on homological algebra
Deleted (so I hope) subjective expressions.
Mar
13
accepted Does the contraction from the localized ring preserve colon ideals and ideal sums/products?
Mar
13
comment Does the contraction from the localized ring preserve colon ideals and ideal sums/products?
Thank you very much for the answer. Especially, the counter examples are wonderful.
Feb
23
comment Vague definitions of ramified, split and inert in a quadratic field
The definition 1. should read "$p$ is ramified in $\mathcal{O}_{K}$ if there is at least one $j$ for which $e_{j} > 1$."
Jan
23
comment Beginner's text for Algebraic Number Theory
I second ndroock1. Stewart and Tall's Algebraic Number Theory and Fermat's Last Theorem is supposed to be an introduction to the subject, but it has several logical gaps that beginners may find hard to fill in. I would choose Alaca and Williams instead.
Nov
1
awarded  Yearling
Jul
17
revised Is $1 : 7 = 1 / 8$ or is it $1/7$?
edited body