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Ideal Theory of Commutative Rings and Monoids : Lecture Notes in Mathematics : Book 2368 - Franz Halter-Koch

Ideal Theory of Commutative Rings and Monoids

By: Franz Halter-Koch, Alfred Geroldinger (Editor), Andreas Reinhart (Editor)

eText | 13 May 2025

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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, Prufer 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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Non-FictionMathematicsAlgebraGroups & Group Theory

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