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(hō′mə-lŏj′ĭ-kəl, hŏm′ə-) also



ho′mo·log′i·cal·ly adv.
References in periodicals archive ?
Rate distortion manifolds pertaining to distinct homotopy types are then expected to represent distinct homologies in relationship to information, intrinsic languages of cognition and culture, and to which such homological techniques can be applied.
Some familiarity with basic homological algebra is needed in the final chapter.
In Section 5 we use homological algebra to study dashings; our main result is the enumeration of odd dashings for any chromotopology.
This two-volume research monograph on the general Lagrangian Floer theory and the accompanying homological algebra of filtered $A_\infty$-algebras provides the most important step towards a rigorous foundation of the Fukaya category in general context.
Research objectives and content The project aims at: Investigating the homological properties (Hoschild and cyclic (co)homology of algebres defined by monominal relations.
Readers are assumed to have a basic knowledge of commutative algebra, homological algebra, and category theory.
In terms of homological algebra, we have a chain complex
An emphasis on homological algebra allows basic notions on complexes to be presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject.
Using standard homological algebra, one can then define [Ext.
Topics include the Boij-Soderberg theory (introduction and survey); Hilbert functions of fat point subschemes of the plane; edge ideals (algebraic and combinatorial properties); three simplicial resolutions; a minimal poset resolution of stable ideals, subsets of complete intersections and the EGH conjecture; the homological conjectures; the compatibility, independence, and linear growth properties; recent progress in coherent rings (a homological perspective); and non-commutative crepant resolutions (scenes from categorical geometry).
In light of the previous proposition, one may consider any one of the four complexes, as its homology determines the homology of the others (either by turning it around in homological degree, or by taking dual [F.
Based on a June 2005 summer school, this series of 24 lectures introduces the algebraic sets, sheaf theory, and homological algebra leading to the definition and alternative characterizations of local cohomology.