Description
This is a book about research in commutative ring theory. It covers a variety of topics in the field, including monoid rings, factorization, irreducibility criteria, class group, integer-valued polynomials, Skolem properties, normsets, Koszul algebras, primary decomposition, Noetherian domains, and the Krull-Schmidt property. It also discusses domains, Prfer domains, GCD-domains, pullbacks, A + XB[X] domains, pseudo-valuation rings, Hermite rings, and semi-Steinitz rings.
Presenting the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco, this up-to-date reference details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examining wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry, Advances in Commutative Ring Theory covers: - monoid rings and the n-generator property - factorization and irreducibility criteria, class group, integer-valued polynomials, Skolem properties, and normsets - Koszul algebras, primary decomposition, Noetherian domains, and the Krull-Schmidt property - domains, Prfer domains, GCD-domains, pullbacks, A + XB[X] domains, pseudo-valuation rings, Hermite rings, and semi-Steinitz rings - Krull and projective dimensions, n-coherence, Kaplansky ideal transform, trace properties, polynomial rings, formal power series rings, seminormality, and root closure - plane cubic curves, spectral topology, and completions
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