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 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