Results 241 to 250 of about 539,595 (279)
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Abelian Groups with a Vanishing Homology Group
Canadian Journal of Mathematics, 1969In this paper, we wish to characterize those abelian groups whose integral homology groups vanish in some positive dimension. We obtain a complete characterization provided the dimension in which the homology vanishes is odd; in fact, we prove that the only abelian groups which possess a vanishing homology group in an odd dimension are, up to ...
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On The Homology Theory Of Abelian Groups
Canadian Journal of Mathematics, 19551. Introduction. In (1) we have introduced the notions of “construction” and “ generic acyclicity” in order to determine a homology theory for any class of multiplicative systems defined by identities. Among these classes the most interesting one is the class of associative and commutative systems II with a unit element (containing the class of abelian
Eilenberg, Samuel, MacLane, Saunders
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ON THE HOMOLOGICAL DIMENSION OF GROUP ALGEBRAS OF SOLVABLE GROUPS
Mathematics of the USSR-Izvestiya, 1971In the paper we calculate the weak dimension of the group algebra of a solvable group and the projective dimension of the group algebra of a countable nilpotent group. Exact bounds are obtained for the projective dimension of the group algebra of a torsion-free solvable group. For the case that the principal ring is commutative and Noetherian we obtain
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On Homology and Cohomology Groups of Remainders
gmj, 2004Abstract Border homology and cohomology groups of pairs of uniform spaces are defined and studied. These groups give an intrinsic characterization of Čech type homology and cohomology groups of the remainder of a uniform space.
Baladze, V., Turmanidze, L.
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1982
In homological algebra one constructs homological invariants of algebraic objects by the following process, or some variant of it:
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In homological algebra one constructs homological invariants of algebraic objects by the following process, or some variant of it:
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On the subsheaves of the sheaf of the homology groups
1997Let \(X\) be a connected complex manifold. For each \(x\in X\), let \(H_x= \pi_1 (X,x)\) and let \({\mathcal H}_x =H_x/N_x\) where \(N_x\) is the commutator subgroup of \(H_x\). The authors obtain a sheaf \(({\mathcal H}, \pi)\) over \(X\). They classify the subsheaves of \({\mathcal H}\).
ÖZDEMİR, Murat, AKBULUT, Sezgin
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