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Introduction to commutative algebra and algebraic geometry. Transl. from the German by Michael Ackerman. With a preface by David Mumford. (English) Zbl 0563.13001
Boston-Basel-Stuttgart: Birkhäuser. X, 238 p. DM 98.00 (1985).
The English text is - except for a few changes - a translation of the German edition of the author’s book ”Einführung in die kommutative Algebra und algebraische Geometrie” (1980; Zbl 0432.13001). Some errors found in the original text have been removed and several passages have been better formulated. In the references the reader’s attention is drawn to new findings that are in direct correlation to the contents of the book; the references were expanded accordingly.

MSC:
13-02 Research exposition (monographs, survey articles) pertaining to commutative algebra
13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
14Axx Foundations of algebraic geometry
14B05 Singularities in algebraic geometry
13B30 Rings of fractions and localization for commutative rings
13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)