From f0846498d1ffc320445feae07eed571522a460ba Mon Sep 17 00:00:00 2001
From: JJ
Date: Thu, 18 Jan 2024 13:51:11 -0800
Subject: meow

---
 mathematics/algebra.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

(limited to 'mathematics/algebra.md')

diff --git a/mathematics/algebra.md b/mathematics/algebra.md
index 5434ff9..5047970 100644
--- a/mathematics/algebra.md
+++ b/mathematics/algebra.md
@@ -14,7 +14,7 @@ these structures are very general: and so results from abstract algebra can be a
 An **algebraic structure** is a set with a collection of *operations* and a finite set of *axioms* those operations must satisfy.
 
 A **group** $G$ is a set with a single binary operation ⋆ satisfying the following axioms:
-- associativity: $∀a,b,c : (a⋆b)⋆c = a⋆(b⋆c)
+- associativity: $∀a,b,c : (a⋆b)⋆c = a⋆(b⋆c)$
 - identity: $∃e, ∀a : e⋆a = a⋆e = a$
 - inverse: $∀a, ∃a^{-1} : a⋆a^{-1} = e$
 - An Abelian or **commutative group** satisfies an additional axiom:
@@ -24,12 +24,12 @@ A **monoid** is a group without an inverse operation.
 
 A **ring** $R$ is a set with two binary operations + and × satisfying the following axioms:
 - $(R, +)$ is a *commutative group*:
-  - associativity: $∀a,b,c : (a+b)+c = a+(b+c)
+  - associativity: $∀a,b,c : (a+b)+c = a+(b+c)$
   - additive identity: $∃0, ∀a : 0+a = a+0 = a$
   - additive inverse: $∀a, ∃-a : a+(-a) = 0$
   - commutativity: $∀a,b : a+b=b+a$
 - $(R, ×)$ is a *monoid*
-  - associativity: $∀a,b,c : (a×b)×c = a×(b×c)
+  - associativity: $∀a,b,c : (a×b)×c = a×(b×c)$
   - multiplicative identity: $∃1, ∀a : 1×a = a×1 = a$
 - The *distributive laws* hold for + and ×:
   - $∀a,b,c : (a+b) × c = (a×c)+(b×c)$
@@ -41,7 +41,7 @@ A **field** is a *commutative ring* where $0 ≠ 1$ and all elements sans $0$ ha
 
 A **vector space** $V$ over a field $F$ of scalars is a set with a binary operation + and a binary function satisfying the following axioms:
 - $(V, +)$ is a *commutative group*:
-  - associativity: $∀u,v,w : (u+v)+w = u+(v+w)
+  - associativity: $∀u,v,w : (u+v)+w = u+(v+w)$
   - additive identity: $∃0, ∀v: 0+v = v+0 = v$
   - additive inverse: $∀v, ∃-v: v+(-v) = 0$
   - commutativity: $∀u,v : u+v=v+u$
-- 
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