Rings and Fields

Start with rings and definitions

Rings and Fields is a section of Abstract Algebra in Mathematics. Its resources focus on definitions, properties and relationships that appear in the unit. The collection consists of flashcard decks and a mind map made by GoConqr users.

For a starting point, use Rings: Intro and Definitions. Its prompts cover ring axioms, an identity and properties involving elements of a ring. Try answering each prompt before looking at the response, then return to any definitions or properties you want to check.

Move from definitions to relationships

The Rings mind map lays out ring axioms, subrings, subring criteria, ideals, principal ideals and cosets. Use it alongside the introductory flashcards to see which ideas appear together. You can then work through Rings: Ideals, which includes prompts on left, proper and trivial ideals.

For homomorphisms, Rings: Homomorphisms asks about ring homomorphisms and the zero homomorphism. Rings: Ideal Homomorphisms includes prompts about kernels and one-to-one homomorphisms. Comparing these decks with the map can help you organize the terms as you study.

Practice with questions and the map

Galois Chapter 1 asks what integral domains and fields are and whether every field is an integral domain. It also includes a question about the characteristic of a field. Use those prompts to check how you describe the terms, then return to the relevant flashcards when you need another look.

There are no quizzes listed on this page. You can write your own questions from the flashcard prompts and use the mind map to organize the ring-related terms around them. This gives you a way to move between recalling a definition and seeing it in the wider Abstract Algebra collection. Choose a deck and use the map alongside it.