Introduction to Axiomatic 33 HIRSCH. Differential Topology. Set Theory. 2nd ed. 34 SPITZER. Principles of Random Walk. 2nd ed. 2 OXTOBY. Measure and Category. 2nd ed. 35 WERMER. Banach Algebras and Several 3 SCHAEFER. Topological Vector Spaces. Complex Variables. 2nd ed. 4 HILTON/STAMMBACH. A Course in 36 KELLEy/NAMIOKA et aL Linear Topological Homological Algebra. Spaces. 5 MAC LANE. Categories for the Working 37 MONK. Mathematical Logic. Mathematician. 38 GRAUERT/FruTZSCHE. Several Complex 6 HUGHES/PIPER. Projective Planes. Variables. 7 SERRE. A Course in Arithmetic. 39 ARVESON. An Invitation to C*-Algebra~. 8 TAKEUTI/ZARING. Axiomatic Set Theory. 40 KEMENy/SNELL/KNAPP. Denumerable Markov 9 HUMPHREYS. Introduction to Lie Algebra~ Chains. 2nd ed. and Representation Theory. 41 ApOSTOL. Modular Functions and Dirichlet 10 COHEN. A Course in Simple Homotopy Series in Number Theory. 2nd ed. Theory. 42 SERRE. Linear Representations of Finite 11 CONWAY. Functions of One Complex Groups. Variable I. 2nd ed. 43 GILLMAN/JERISON. Rings of Continuous 12 BEALS. Advanced Mathematical Analysis. Functions. \3 ANDERSON/FULLER. Rings and Categories of 44 KENDIG. Elementary Algebraic Geometry. Modules. 2nd ed. 45 LOEVE. Probability Theory I. 4th ed. 14 GOLUBITSKy/GUILLEMIN. Stable Mappings 46 LOEVE. Probability Theory II. 4th ed. and Their Singularities. 47 MOISE. Geometric Topology in Dimensions 2 15 BERBERIAN. Lectures in Functional Analysis and 3. and Operator Theory. 48 SACHSIWu. General Relativity for 16 WINTER. The Structure of Fields. Mathematicians. 17 ROSENBLATT. Random Processes. 2nd ed. 49 GRUENBERGIWEIR. Linear Geometry. 2nd ed. 18 HALMos. Measure Theory. 50 EDWARDS. Fermat's Last Theorem. 19 HALMos. A Hilbert Space Problem Book. 51 KLINGENBERG. A Course in Differential 2nd ed. Geometry. 20 HUSEMOLLER. Fibre Bundles. 3rd ed. 52 HARTSHORNE. Algebraic Geometry. 21 HUMPHREYS. Linear Algebraic Groups. 53 MANIN. A Course in Mathematical Logic. 22 BARNES/MACK. An Algebraic Introduction to 54 GRAVERIW ATKINS. Combinatorics with Mathematical Logic. Emphasis on the Theory of Graphs. 23 GREUB. Linear Algebra. 4th ed. 55 BROWN/PEARCY. Introduction to Operator 24 HOLMES. Geometric Functional Analysis and Theory I: Elements of Functional Analysis. Its Applications.

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We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and it has numerous applications within and beyond pure mathematics. The ideals defining toric varieties are precisely the binomial prime ideals.Our main results concern primary decomposition: If I is a binomial ideal then the radical, associated primes, and isolated primary components of I are again binomial, and I admits primary decompositions in terms of binomial primary ideals. A geometric characterization is given for the affine algebraic sets that can be defined by binomials. Our structural results yield sparsity-preserving algorithms for finding the radical and primary decomposition of a binomial ideal.

Abstract.Let R be a regular local ring, and let A = R/(x), where x is any nonunit of R. We prove that every minimal free resolution of a finitely generated A -module becomes periodic of period 1 or 2 after at most dim A steps, and we examine generalizations and extensions of this for complete intersections. Our theorems follow from the properties of certain universally defined endomorphisms of complexes over such rings.

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