What are the best books for understanding universal algebra?

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SUMMARY

The discussion centers on the best resources for understanding universal algebra, particularly for individuals with a background in algebra and topology. It clarifies that universal algebra aims to unify various algebraic structures, similar to category theory, but with a more focused approach. The recommended primary resource is the free book by Burris and Sankappanavar, which provides a comprehensive introduction to the subject. The discussion emphasizes that universal algebra seeks to establish a general definition of algebraic objects and prove broad isomorphism theorems.

PREREQUISITES
  • Familiarity with algebraic structures such as rings, vector spaces, and groups
  • Understanding of category theory concepts
  • Knowledge of isomorphism theorems
  • Background in advanced algebra texts, such as Herstein's "Topics in Algebra"
NEXT STEPS
  • Read the free book "Universal Algebra" by Burris and Sankappanavar
  • Explore the concepts of isomorphism theorems in greater depth
  • Investigate the relationship between universal algebra and category theory
  • Study additional resources on algebraic structures to enhance foundational knowledge
USEFUL FOR

Mathematicians, graduate students, and educators seeking to deepen their understanding of universal algebra and its applications in various algebraic contexts.

bacte2013
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What are good books in universal algebra, given that I have a background in Herstein (Topics in Algebra), Hubbard/Hubbard, Engelking (Topology), and Dugundji (Topology)? I am currently reading Hungerford, and I found a field called universal algebra while searching internet for some concepts. Is universal algebra basically "algebra done right"?
 
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bacte2013 said:
Is universal algebra basically "algebra done right"?

No, it's not.

Universal algebra has pretty much the same goals as category theory, but a bit more modest. Basically, universal algebra attempts to give a unifying structure for all algebraic structures. The need for this comes from recognizing that both rings, vector spaces and groups have their own version of the isomorphism theorems. One of the goals of universal algebra is to give a general definition of an algebraic object and to prove the most general possible isomorphism theorems.

The best book in this field is probably the free book by Burris and Sankappanavar: http://www.math.hawaii.edu/~ralph/Classes/619/univ-algebra.pdf
 

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