---
title: Homomorphisms
description: Homomorphisms are structure-preserving maps between algebraic systems such as groups or rings. Learners will understand how to define these mappings, apply the isomorphism theorems, and analyze how algebraic properties are transferred or preserved between different mathematical structures.
category: mathematics
subcategory: abstract-algebra
difficulty: beginner, intermediate, advanced
url: /subject/homomorphisms
---

# Homomorphisms

Homomorphisms are structure-preserving maps between algebraic systems such as groups or rings. Learners will understand how to define these mappings, apply the isomorphism theorems, and analyze how algebraic properties are transferred or preserved between different mathematical structures.

## Available Resources

1 Courses • 2 Websites

## Websites

### 1. nLab: Homomorphism

Wiki entry defining homomorphisms as structure-preserving maps between algebraic structures and relating them to morphisms in a category, with links to monomorphisms, isomorphisms, and related notions. Suits readers who already know basic algebra and want the categorical framing.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/homomorphism

**Tags:** homomorphisms, category-theory, abstract-algebra, morphisms

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Abstract Algebra

Learn abstract algebra homomorphisms with Prof. Benedict Gross! Explore key concepts in this insightful course.

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLzUeAPxtWcqzr80lS25FrzMn7a36BuXhj

**Tags:** abstract-algebra, group-theory, homomorphisms, ring-theory

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