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Record Nr. |
UNINA9911002560403321 |
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Autore |
Halter-Koch Franz <1944-2023> |
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Titolo |
Ideal Theory of Commutative Rings and Monoids / / by Franz Halter-Koch ; edited by Alfred Geroldinger, Andreas Reinhart |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
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ISBN |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (X, 282 p. 1 illus.) |
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Collana |
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Lecture Notes in Mathematics, , 1617-9692 ; ; 2368 |
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Disciplina |
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Soggetti |
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Commutative algebra |
Commutative rings |
Group theory |
Commutative Rings and Algebras |
Group Theory and Generalizations |
Anells commutatius |
Monoides |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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- 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. |
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Sommario/riassunto |
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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. |
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