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"Ring and field theory" denotes books focused on the algebraic study of rings, fields, and their related structures and morphisms. Works in this category range from introductory undergraduate texts that introduce rings, ideals, homomorphisms, polynomial rings and basic field extensions to advanced treatments of commutative algebra, valuation theory, Galois theory, algebraic number theory, and their connections to algebraic geometry and homological methods. The category includes textbooks, lecture notes, problem books, and research monographs that develop structural results (e.g., factorization, modules, Noetherian/Artinian conditions), explicit computations (splitting fields, finite fields), and applications (coding theory, cryptography, arithmetic geometry). Typical readers are students of abstract algebra and graduate students or researchers in pure mathematics, though accessible introductions and applied-oriented texts serve a broader audience.

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