Difference between revisions of "817 - Algebra"
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==Rings== | ==Rings== | ||
| + | '''Definition:''' A ring is a set <math>R</math> with two binary operation <math> +</math> and <math>\cdot</math> satisfying: | ||
| + | # <math> (R,+)</math> is an abelian group (with identity 0) | ||
| + | # <math> (R,\cdot) </math> is a semigroup | ||
| + | # <math>\cdot </math> is distributive over <math> + </math> (on both sides) | ||
Revision as of 02:46, 7 December 2022
Contents
Groups
Theorems
Topics in Group Theory
Sylow Theory
Semi-Direct Product
Quotient Groups
Isomorphism Theorems
Rings
Definition: A ring is a set \(R\) with two binary operation \( +\) and \(\cdot\) satisfying:
- \( (R,+)\) is an abelian group (with identity 0)
- \( (R,\cdot) \) is a semigroup
- \(\cdot \) is distributive over \( + \) (on both sides)
