منابع مشابه
1 6 O ct 1 99 3 PROJECTIVE RESOLUTIONS FOR GRAPH PRODUCTS
Let Γ be a finite graph together with a group Gv at each vertex v. The graph product G(Γ) is obtained from the free product of all Gv by factoring out by the normal subgroup generated by {ghgh; g ∈ Gv, h ∈ Gw} for all adjacent v, w. In this note we construct a projective resolution for G(Γ) given projective resolutions for each Gv, and obtain some applications. Let Γ be a finite graph together ...
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In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this ...
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The category of crossed complexes gives an algebraic model of CW -complexes and cellular maps. Free crossed resolutions of groups contain information on a presentation of the group as well as higher homological information. We relate this to the problem of calculating non-abelian extensions. We show how the strong properties of this category allow for the computation of free crossed resolutions...
متن کاملExistence of Gorenstein Projective Resolutions
Gorenstein rings are important to mathematical areas as diverse as algebraic geometry, where they encode information about singularities of spaces, and homotopy theory, through the concept of model categories. In consequence, the study of Gorenstein rings has led to the advent of a whole branch of homological algebra, known as Gorenstein homological algebra. This paper solves one of the open pr...
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The problem of explicitly finding a free resolution, minimal in some suitable sense, of a module over a polynomial ring is solved in principle by the algorithm of Hilbert [H]. However, this algorithm is of enormous computational difficulty. If the module happens to be finite dimensional over the ground field, and if the module structure is given by specifying the commuting linear transformation...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1995
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500006313