From 93689618c67e8d6f5db9702097d614d3fbd1ab57 Mon Sep 17 00:00:00 2001
From: JJ
Date: Sun, 17 Mar 2024 13:26:54 -0700
Subject: meow

---
 mathematics/algebra.md | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

(limited to 'mathematics')

diff --git a/mathematics/algebra.md b/mathematics/algebra.md
index 1da221b..0ba7847 100644
--- a/mathematics/algebra.md
+++ b/mathematics/algebra.md
@@ -5,8 +5,7 @@ title: mathematics/algebra
 
 # algebra
 
-modern algebra is the study of **algebraic structures**: groups, rings, fields, modules, and the like.
-these structures are very abstract: and so results can be applied to a wide variety of situations.
+Modern algebra is the study of **algebraic structures**: groups, rings, fields, modules, and the like. These structures are very abstract: and so results can be applied to a wide variety of situations.
 
 ## structures
 
@@ -45,8 +44,8 @@ A **vector space** $V$ over a field $F$ of scalars is a set with a binary operat
   - additive inverse: $∀v, ∃-v: v+(-v) = 0$
   - commutativity: $∀u,v : u+v=v+u$
 - $(V, )$ is a *scalar operation*:
-  - scalar identity: $∃1 ∈ F : 1v = v1 = v$
-  - commutativity: $∀a,b ∈ F, ∀v ∈ V (ab)v = a(bv)$
+  - scalar identity: $∃1 ∈ F, ∀v ∈ V : 1v = v1 = v$
+  - commutativity: $∀a,b ∈ F, ∀v ∈ V : (ab)v = a(bv)$
 - The *distributive laws* hold:
   - $∀a ∈ F, ∀u,v ∈ V : a(u+v) = au+av$
   - $∀a,b ∈ F, ∀v ∈ V : (a+b)v = av + bv$
-- 
cgit v1.2.3-70-g09d2