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This subtopic studies generalizations of field theory, including broader algebraic systems where field-like methods still provide insight into structure and extension problems.
12K05 develops near-fields within generalizations of field theory. It emphasizes foundational definitions, structural theorems, and techniques that support both proof-oriented and computational workflows.
Used to classify algebraic structures, transfer properties across extensions and localizations, and organize arguments in commutative algebra and algebraic geometry.
12K10 develops semifields within generalizations of field theory. It emphasizes foundational definitions, structural theorems, and techniques that support both proof-oriented and computational workflows.
Used to classify algebraic structures, transfer properties across extensions and localizations, and organize arguments in commutative algebra and algebraic geometry.