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Ordered algebraic structures --- Noncommutative rings --- Congresses. --- 51 --- -Non-commutative rings --- Associative rings --- Mathematics --- Congresses --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Non-commutative rings --- Noncommutative rings - Congresses.
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The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.
Cohen-Macaulay rings. --- Cohen-Macaulay modules. --- Macaulay modules, Cohen --- -Modules (Algebra) --- Macaulay local rings --- Macaulay rings, Cohen --- -Rings, Cohen-Macaulay --- Rings, Macaulay local --- Local rings --- Matsumura, Hideyuki, --- Matsumura, H. --- 松村英之, --- Ordered algebraic structures
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Filters (Mathematics) --- Ideals (Algebra) --- Polyhedral functions --- Rings (Algebra)
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Continuous and discrete modules are, essentially, generalizations of infective and projective modules respectively. Continuous modules provide an appropriate setting for decomposition theory of von Neumann algebras and have important applications to C*-algebras. Discrete modules constitute a dual concept and are related to number theory and algebraic geometry: they possess perfect decomposition properties. The advantage of both types of module is that the Krull-Schmidt theorem can be applied, in part, to them. The authors present here a complete account of the subject and at the same time give a unified picture of the theory. The treatment is essentially self-contained, with background facts being summarized in the first chapter. This book will be useful therefore either to individuals beginning research, or the more experienced worker in algebra and representation theory.
Injective modules (Algebra) --- Projective modules (Algebra) --- Representations of rings (Algebra) --- Decomposition (Mathematics) --- Mathematics --- Probabilities --- Rings (Algebra) --- Modules (Algebra)
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512.71 --- 512.55 --- #WWIS:d.d. Frank Laforce --- #WWIS:ALTO --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Rings and modules --- 512.55 Rings and modules --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative algebra --- Algebra --- Algèbres commutatives
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Physics --- Mathematics --- Geometry, Algebraic --- Grothendieck, Alexandre, --- 512.7 --- Algebraic geometry --- Geometry --- Algebraic geometry. Commutative rings and algebras --- Grothendieck, A. --- Festschrift - Libri Amicorum --- 512.7 Algebraic geometry. Commutative rings and algebras --- Grothendieck, Alexandre --- Grothendieck, Alexander --- Raddatz, Alexander --- Grothendieck, Alexandre, - 1928-2014
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A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students.
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Ordered algebraic structures --- Algebres regulieres --- Anneaux de groupes --- Groepsringen --- Group rings --- Modulaire representaties van groepen --- Modular representations of groups --- Reguliere algebra's --- Representations modulaires de groupes --- Tame algebras --- Modular representations of groups. --- Group rings. --- Tame algebras. --- 51 --- Algebras, Tame --- Associative algebras --- Representations of groups --- Group theory --- Rings (Algebra) --- Mathematics --- 51 Mathematics
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