User contributions
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- 16:46, 8 March 2023 diff hist +889 Free Modules
- 16:45, 8 March 2023 diff hist -762 Main Page current
- 16:44, 8 March 2023 diff hist +762 Main Page →Math
- 05:54, 8 March 2023 diff hist +165 N Free Modules Created page with " '''Definition:''' A subset A of an R-module M is a basis of M if A is linearly independent and generates M. An R-module M is a '''free''' R-module if M has a basis."
- 01:30, 8 March 2023 diff hist +341 N Modules Created page with "Definition and examples: matrices, free modules, and bases over arbitrary commutative rings, Structure Theorem for finitely generated modules over PIDs, applications to linear..."
- 01:25, 8 March 2023 diff hist +4 Algebra Qualifying Syllabus
- 01:14, 8 March 2023 diff hist +152 N Category:Ring Theory Created page with "Topics on the qual: Definition and examples, homomorphisms, ideals, quotients, integral domains and their fields of fractions, maximal and prime ideals." current
- 01:12, 8 March 2023 diff hist +27 Principle Ideal Domains current
- 01:12, 8 March 2023 diff hist +29 Integral Domains current
- 01:12, 8 March 2023 diff hist +28 Prime Ideals current
- 01:11, 8 March 2023 diff hist +28 N Isomorphism Theorems Created page with " Category: Group Theory" current
- 01:09, 8 March 2023 diff hist +33 Semi-Direct Product current
- 01:06, 8 March 2023 diff hist +28 Sylow Theory current
- 01:05, 8 March 2023 diff hist +7 m Algebra Qualifying Syllabus
- 01:03, 8 March 2023 diff hist +1,725 N Algebra Qualifying Syllabus Created page with "'''Group Theory:''' Groups, subgroups, homomorphisms, cosets, quotients, isomorphism theorems, direct and semidirect products, solvable groups, structure of cyclic, symmetric..."
- 01:02, 8 March 2023 diff hist +32 Fall 2022 Classes →Course list
- 18:44, 6 March 2023 diff hist +1 Fall 2022 Classes
- 18:44, 6 March 2023 diff hist +18 Fall 2022 Classes →Course list
- 20:47, 17 January 2023 diff hist +10 Prime Ideals
- 20:46, 17 January 2023 diff hist +729 Prime Ideals
- 20:45, 17 January 2023 diff hist +66 N Integral Domains Created page with ":''return to Algebra main page"
- 20:44, 17 January 2023 diff hist +3 817 - Algebra →Integral Domains current
- 20:41, 17 January 2023 diff hist +62 N Prime Ideals Created page with ":''return to Algebra main page"
- 20:40, 17 January 2023 diff hist +4 817 - Algebra →Prime Ideals
- 20:39, 17 January 2023 diff hist +69 N Semi-Direct Product Created page with ":''return to Algebra main page"
- 20:38, 17 January 2023 diff hist -34 817 - Algebra →Semi-Direct Product
- 20:38, 17 January 2023 diff hist +62 Sylow Theory
- 20:36, 17 January 2023 diff hist -26 817 - Algebra →Sylow Theory
- 20:35, 17 January 2023 diff hist +1 Principle Ideal Domains
- 20:34, 17 January 2023 diff hist +46 Principle Ideal Domains
- 20:25, 17 January 2023 diff hist +933 N Principle Ideal Domains Created page with "A ''Principal Ideal Domain'' (PID) is a domain, <math>R</math> with the property that every ideal is principal, i.e., for each ideal <math>I</math>, we have <math>I = (a) </ma..."
- 20:01, 17 January 2023 diff hist +1,015 817 - Algebra →Named Rings
- 19:49, 17 January 2023 diff hist +475 N Integral Domain Created page with "An 'Integral Domain', often just called domain, is a commutative ring <math>R </math>, with <math>1\neq 0 </math> and has no zero divisors. Any unital subring of an integral..." current
- 15:50, 16 January 2023 diff hist +433 Sylow Theory →Sylow Theorem 1 (Existence)
- 15:41, 16 January 2023 diff hist -1 817 - Algebra →Sylow Theory
- 15:03, 16 January 2023 diff hist +589 817 - Algebra →Sylow Theory
- 14:58, 16 January 2023 diff hist +28 817 - Algebra →Groups
- 07:17, 12 January 2023 diff hist +469 N Metrizability Created page with " A topological space <math> (X,\mathcal{T}_X) </math> is metrizable if there is a metric <math>d </math> on <math> X</math> such that <math>\mathcal{T}_X = \mathcal{T}_d </mat..." current
- 19:14, 7 January 2023 diff hist +2 871 - Topology →Metrizability
- 19:11, 7 January 2023 diff hist +500 871 - Topology →Metrizability
- 17:57, 14 December 2022 diff hist +198 825 - Analysis →Completeness Axioms current
- 23:16, 11 December 2022 diff hist +8 m Semi-Direct Products current
- 23:14, 11 December 2022 diff hist 0 Semi-Direct Products
- 23:12, 11 December 2022 diff hist +251 Semi-Direct Products
- 03:09, 8 December 2022 diff hist +122 N Field Created page with " A ring <math>R </math> is a ''field'' if every nonzero element is a unit. Thus field implies domain." current
- 23:35, 7 December 2022 diff hist +6 Semi-Direct Products
- 23:34, 7 December 2022 diff hist +345 N Semi-Direct Products Created page with " Let <math>H </math> and <math> K</math> be groups and let <math>\rho:K\to \Aut(H) </math> be a homomorphism. The (external) semidirect product induced by <math>\rho </math> i..."
- 23:05, 7 December 2022 diff hist +77 817 - Algebra
- 21:25, 7 December 2022 diff hist +172 N Sequences (Analysis) Created page with " ===Bolzano-Weirstrass Theorem=== If <math> \{a_n\}\sube \R</math> is a bounded sequence, there exists a convergent subsequence <math> \{a_{n_k}\} \sube \{a_n\} </math>." current
- 20:49, 7 December 2022 diff hist -18 871 - Topology →Homeomorphism Invariants
