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"Polynomial rings" is a book category devoted to the algebraic study and applications of rings of polynomials — from introductory treatments of univariate polynomials to advanced monographs on multivariate rings over fields and general commutative rings. Volumes in this category cover core structural topics (ideals, factorization, unique factorization domains, Noetherian rings, Hilbert's Basis Theorem, syzygies), key theorems connecting to algebraic geometry (Hilbert's Nullstellensatz, coordinate rings), computational and algorithmic methods (Gröbner bases, resultants, eliminations), and applied perspectives (coding theory, cryptography, computational algebra systems). It embraces textbooks, problem books, lecture notes, and research expositions aimed at undergraduates learning abstract algebra, graduate students specializing in commutative algebra or algebraic geometry, and researchers seeking deeper theoretical or computational tools. Readers can expect a mix of theory, examples, exercises, and concrete algorithms that illuminate how polynomial rings organize algebraic information and underpin many areas of modern mathematics.

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