User contributions for Hbghlyj
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2 May 2024
- 09:0809:08, 2 May 2024 diff hist +52 Isomorphism between Group of Units Ring of Integers Modulo 2^n and C2 x C2^(n-2) Extracted a lemma current
- 07:0407:04, 2 May 2024 diff hist +3 Group of Units Ring of Integers Modulo p^2 is Cyclic added category
- 06:5906:59, 2 May 2024 diff hist +5 m Group of Units Ring of Integers Modulo p^2 is Cyclic x should be \times
1 May 2024
- 12:5012:50, 1 May 2024 diff hist −59 Group of Units Ring of Integers Modulo p^2 is Cyclic {{explain|Why is this not being developed in a sandbox?}} Explanation: I used the preview button before saving changes. I think preview has similar function as sandbox. Tag: Manual revert
- 12:1012:10, 1 May 2024 diff hist −10 m Group of Units Ring of Integers Modulo p^2 is Cyclic No edit summary
- 12:1012:10, 1 May 2024 diff hist +13 m Group of Units Ring of Integers Modulo p^2 is Cyclic Typo
- 12:0912:09, 1 May 2024 diff hist +4 m Group of Units Ring of Integers Modulo p^2 is Cyclic adjust numbering
- 12:0712:07, 1 May 2024 diff hist +61 Group of Units Ring of Integers Modulo p^2 is Cyclic add more explanation
- 12:0412:04, 1 May 2024 diff hist +2 m Group of Units Ring of Integers Modulo p^2 is Cyclic add more words
- 12:0312:03, 1 May 2024 diff hist +3,335 N Group of Units Ring of Integers Modulo p^2 is Cyclic Created page with "== Theorem == Let $p$ be a prime. Let $\struct {\Z / p^2 \Z, +, \times}$ be the ring of integers modulo $p^2$. Let $U = \struct {\paren {\Z / p^2 \Z}^\times, \times}$ denote the group of units of $\struct {\Z / p^2 \Z, +, \times}$. Then $U$ is cyclic. == Proof == The case $p = 2$ follows from Isomorp..."
- 11:3211:32, 1 May 2024 diff hist +55 m Cyclicity Condition for Units of Ring of Integers Modulo n No edit summary
- 11:2911:29, 1 May 2024 diff hist −9 m Cyclicity Condition for Units of Ring of Integers Modulo n Typo
- 11:2911:29, 1 May 2024 diff hist +150 Cyclicity Condition for Units of Ring of Integers Modulo n No edit summary
- 11:2211:22, 1 May 2024 diff hist +163 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 No edit summary Tag: Reverted
- 11:1511:15, 1 May 2024 diff hist +51 Cyclicity Condition for Units of Ring of Integers Modulo n Add link to a nonexistent page Group of Units of a Finite Field is Cyclic
- 11:1111:11, 1 May 2024 diff hist +15 m Cyclicity Condition for Units of Ring of Integers Modulo n No edit summary
- 11:0511:05, 1 May 2024 diff hist −211 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 No edit summary
- 11:0311:03, 1 May 2024 diff hist +212 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 The lemma is only needed in proof 1, so I move it to prove 1
- 11:0311:03, 1 May 2024 diff hist −212 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n The lemma is only needed in proof 1, so I move it to prove 1 current Tag: Manual revert
- 11:0211:02, 1 May 2024 diff hist −74 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 Fixed {{WIP| prove that no other value of $n$ satisfies $\map\phi n {{=}} 8$}}
- 11:0011:00, 1 May 2024 diff hist −30 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Lemma No edit summary
- 11:0011:00, 1 May 2024 diff hist +662 N Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Lemma Created page with "=== Lemma === There are only $5$ numbers $n$ with the property that $\map \phi n = 8$, and they are $15$, $16$, $20$, $24$ and $30$. === Proof of lemma === Let $p$ be a prime factor of $n$. By Euler Phi Function is Multiplicative: :$p - 1 = \map \phi p \divides \map \phi n = 8$ so $p \in \set{2, 3, 5}$. Let $i,j,k \in \Z^{\ge 0}$ such that $n = 2^i 3^j 5^k$. By Euler Phi Function is Multiplicative: :$8 = \map \phi n = \map \phi {..."
- 10:5910:59, 1 May 2024 diff hist −590 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 Undo revision 692860 by Hbghlyj (talk) Tag: Undo
- 10:5810:58, 1 May 2024 diff hist +590 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1 fix {{WIP| prove that no other value of $n$ satisfies $\map\phi n {{=}} 8$}}
- 10:5510:55, 1 May 2024 diff hist +782 Cyclicity Condition for Units of Ring of Integers Modulo n No edit summary
- 10:4210:42, 1 May 2024 diff hist +9 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n add "we get"
- 10:4210:42, 1 May 2024 diff hist +779 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n Add proof 2
- 10:3210:32, 1 May 2024 diff hist +64 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n Add links
- 10:3010:30, 1 May 2024 diff hist +10 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n No edit summary
- 10:3010:30, 1 May 2024 diff hist +388 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n add a proof of lemma
- 10:1910:19, 1 May 2024 diff hist +7 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n typo
- 10:1810:18, 1 May 2024 diff hist 0 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n typo
- 10:1810:18, 1 May 2024 diff hist 0 m Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n typo?
- 10:1710:17, 1 May 2024 diff hist +2,051 Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n add a proof
- 10:0210:02, 1 May 2024 diff hist −1 m Cyclicity Condition for Units of Ring of Integers Modulo n fix latex error
- 09:5709:57, 1 May 2024 diff hist +1 m Order of 5 in Units of Ring of Integers Modulo 2^n typo current
- 09:5609:56, 1 May 2024 diff hist 0 m Order of 5 in Units of Ring of Integers Modulo 2^n No edit summary
- 09:5609:56, 1 May 2024 diff hist −110 m Order of 5 in Units of Ring of Integers Modulo 2^n No edit summary
- 09:5409:54, 1 May 2024 diff hist +1,832 Order of 5 in Units of Ring of Integers Modulo 2^n Add proof 2
- 09:1709:17, 1 May 2024 diff hist +26 m Isomorphism between Group of Units Ring of Integers Modulo 2^n and C2 x C2^(n-2) add more explanation
- 09:1009:10, 1 May 2024 diff hist −46 Isomorphism between Group of Units Ring of Integers Modulo 2^n and C2 x C2^(n-2) fixed {{mistake|inappropriate use of commas}}
- 08:4908:49, 1 May 2024 diff hist +58 Order of 5 in Units of Ring of Integers Modulo 2^n fixed {{tidy|use the eqn template}}
- 08:1908:19, 1 May 2024 diff hist +1,547 Order of 5 in Units of Ring of Integers Modulo 2^n Add proof
- 07:5007:50, 1 May 2024 diff hist +36 Isomorphism between Group of Units Ring of Integers Modulo 2^n and C2 x C2^(n-2) Add a link
28 April 2024
- 17:2417:24, 28 April 2024 diff hist +65 Euler Phi Function by Argument is Injective Suggestion to Rename
21 April 2024
- 16:0816:08, 21 April 2024 diff hist 0 m Ideal Contained in Finite Union of Prime Ideals the published year is 1989 on Amazon, but 1986 on Wikipedia, so I changed to 1986 current
- 16:0316:03, 21 April 2024 diff hist +204 N Talk:Ideal Contained in Finite Union of Prime Ideals →Other name?: new section
- 16:0216:02, 21 April 2024 diff hist +147 Ideal Contained in Finite Union of Prime Ideals add a BookReference
17 April 2024
- 17:3117:31, 17 April 2024 diff hist 0 m Definition:Coequalizer fix typo "z \circ f = z \circ f" current
- 17:3017:30, 17 April 2024 diff hist +17 m Definition:Coequalizer Add <nowiki> to fix latex errors