LEADER 05900nam 22007215 450 001 9910299970503321 005 20260415134710.0 010 $a1-4939-0925-8 024 7 $a10.1007/978-1-4939-0925-4 035 $a(CKB)3710000000202320 035 $a(EBL)1782046 035 $a(OCoLC)893332483 035 $a(SSID)ssj0001296166 035 $a(PQKBManifestationID)11679695 035 $a(PQKBTitleCode)TC0001296166 035 $a(PQKBWorkID)11347926 035 $a(PQKB)10605608 035 $a(MiAaPQ)EBC1782046 035 $a(DE-He213)978-1-4939-0925-4 035 $a(PPN)179922262 035 $a(EXLCZ)993710000000202320 100 $a20140715d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCommutative Algebra $eRecent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions /$fedited by Marco Fontana, Sophie Frisch, Sarah Glaz 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (372 p.) 300 $aDescription based upon print version of record. 311 08$a1-4939-0924-X 320 $aIncludes bibliographical references. 327 $aPreface -- Weak global dimension of Prüfer-like rings (K. Adarbeh, S -- E. Kabbaj) -- Quasi-complete semilocal rings and modules (D.D. Anderson) -- On the total graph of a ring and its related graphs: A survey (A. Badawi) -- Prime ideals in polynomials and power series rings over Noetherian domains -- Integer-valued polynomials: Looking for regular bases (J -- L. Chabert) -- On Boolean subrings of rings (I. Chajda, G. Eigenthaler) -- On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet-L'Hermitte) -- The probability that Intn(D) is free (J. Elliott) -- Some closure operations in Zariski-Riemann spaces of valuation domains: A survey (C.A. Finocchiaro, M. Fontana, K.A. Loper) -- Ten problems on stability of domains (S. Gabelli) -- The Development of non-Noetherian grade and its applications (L. Hummel) -- Stable homotopy theory, formal group laws, and integer-valued polynomials (K. Johnson) -- How to construct huge chains of prime ideals in power series rings (B.G. Kang, P.T. Toan) -- Localizing global properties to individual maximal idals (T.G. Lucas) -- Prime ideals that satisfy Hensel's Lemma (S. McAdam) -- Finitely stable rings (B. Olberding) -- Integral closure of rings of integer-valued polynomials on algebras (G. Peruginelli, N.J. Werner) -- On monoids and domains whose monadic submonoids are Krull (A. Reinhart) -- Integral closure (I. Swanson) -- Open problems in commutative ring theory (P -- J. Cahen, M. Fontana, S. Frisch, S. Glaz). 330 $aThis volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: ·    Homological dimensions of Prüfer-like rings ·    Quasi complete rings ·    Total graphs of rings ·    Properties of prime ideals over various rings ·    Bases for integer-valued polynomials ·    Boolean subrings ·    The portable property of domains ·    Probabilistic topics in Intn(D) ·    Closure operations in Zariski-Riemann spaces of valuation domains ·    Stability of domains ·    Non-Noetherian grade ·    Homotopy in integer-valued polynomials ·    Localizations of global properties of rings ·    Topics in integral closure ·    Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere. 606 $aCommutative algebra 606 $aCommutative rings 606 $aCategories (Mathematics) 606 $aAlgebra, Homological 606 $aAlgebraic topology 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aCategories (Mathematics) 615 0$aAlgebra, Homological. 615 0$aAlgebraic topology. 615 14$aCommutative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 615 24$aAlgebraic Topology. 676 $a510 676 $a512 676 $a512 .44 676 $a512.44 702 $aFontana$b Marco$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aFrisch$b Sophie$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGlaz$b Sarah$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910299970503321 996 $aCommutative algebra$980108 997 $aUNINA