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Algebraic geometry --- 512.71 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- 512.71 Commutative rings and algebras. Local theory. Foundations of algebraic geometry --- Commutative algebra --- Geometry, Algebraic

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Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience.   Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Ordered algebraic structures --- Algebraic geometry --- algebra --- landmeetkunde --- wiskunde --- geometrie --- Geometry, algebraic. --- Algebra. --- Algebraic Geometry. --- Commutative Rings and Algebras. --- Mathematics --- Mathematical analysis --- Geometry --- Commutative algebra. --- Geometry, Algebraic. --- Algebraic geometry. --- Commutative rings. --- Algebra --- Rings (Algebra)

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Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience.   Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Ordered algebraic structures --- Algebraic geometry --- algebra --- landmeetkunde --- wiskunde --- geometrie

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This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading. Most important to this text: * Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves * Presents residue theory in the affine plane and its applications to intersection theory * Methods of proof for the Riemann-Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook From a review of the German edition: "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students ¦ The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation ¦highly enlightening, motivating and entertaining at the same time ¦ One simply cannot do better in writing such a textbook." Zentralblatt MATH

Ordered algebraic structures --- Algebra --- Algebraic topology --- Geometry --- Mathematics --- Classical mechanics. Field theory --- algebra --- landmeetkunde --- topologie (wiskunde) --- toegepaste wiskunde --- mechanica

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