03089nam 22006495 450 991100256040332120260128130819.03-031-88878-210.1007/978-3-031-88878-6(CKB)38776241000041(DE-He213)978-3-031-88878-6(MiAaPQ)EBC32111102(Au-PeEL)EBL32111102(OCoLC)1524421193(PPN)285241842(EXLCZ)993877624100004120250514d2025 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierIdeal Theory of Commutative Rings and Monoids /by Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart1st ed. 2025.Cham :Springer Nature Switzerland :Imprint: Springer,2025.1 online resource (X, 282 p. 1 illus.)Lecture Notes in Mathematics,1617-9692 ;23683-031-88877-4 - 1. Basic Monoid Theory -- 2. The Formalism of Module and Ideal Systems -- 3. Prime and Primary Ideals and Noetherian Conditions -- 4. Invertibility, Cancellation and Integrality -- 5. Arithmetic of Cancellative Mori Monoids -- 6. Ideal Theory of Polynomial Rings.This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.Lecture Notes in Mathematics,1617-9692 ;2368Commutative algebraCommutative ringsGroup theoryCommutative Rings and AlgebrasGroup Theory and GeneralizationsAnells commutatiusthubMonoidesthubLlibres electrònicsthubCommutative algebra.Commutative rings.Group theory.Commutative Rings and Algebras.Group Theory and Generalizations.Anells commutatiusMonoides512.44Halter-Koch Franz1944-2023authttp://id.loc.gov/vocabulary/relators/aut1848507Geroldinger Alfrededthttp://id.loc.gov/vocabulary/relators/edtReinhart Andreas(Researcher)edthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9911002560403321Ideal Theory of Commutative Rings and Monoids4435566UNINA