Multiplicative ideal theory and factorization theory : commutative and non-commutative perspectives
著者
書誌事項
Multiplicative ideal theory and factorization theory : commutative and non-commutative perspectives
（Springer proceedings in mathematics & statistics, v. 170）
Springer, c2016
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注記
Other editors : Marco Fontana, Alfred Geroldinger, Bruce Olberding
Includes bibliographical references and index
内容説明・目次
内容説明
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22-26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prufer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
目次
Multiplicative Ideal Theory in Non-commutative Rings (E. Akalan, H. Marubayashi).- About number fields with Polya group of order 2 (D. Adam, J.-L. Chabert).- The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics (K. Cziczler, M. Domokos, A. Geroldinger).- Ring and semigroup constructions (M. D'Anna).- New Distinguished Classes of Spectral Spaces (C.A. Finocchiaro, M. Fontana, D. Spirito).- Relative polynomial closure and monadically Krull monoids of integer-valued polynomials (S. Frisch).-An overview of the computational aspects of nonunique factorization invariants (P.A. Garcia-Sanchez).-Arithmetic of Mori domains and monoids: The global case (F. Kainrath).- Prufer Domains of Integer-Valued Polynomials (K.A. Loper, M. Syvuk).- Lobal Properties of Integral Domains (T.G. Lucas).- Topological aspects of irredundant intersections of ideals and valuation rings (B. Olberding).- Noetherian semigroup algebras and beyond (J. Okninski).- Idempotent pairs and PRINC domains (G. Peruginelli, L. Salce, P. Zanardo).- Some recent results and open problems on sets of lengths of Krull monoids with finite class group (W.A. Schmid).- Factorizations of elements in noncommutative rings: A survey (D. Smertnig).
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