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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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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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Homology of the Infinite Symmetric Group
The Annals of Mathematics, 1961H*(S(co); Z.,) with coefficients in the integers mod p (p :prime). It is proved that the height of any non-zero element is co if p = 2, and is either co or < p if p is odd. If p = 2 this fact and the result in [11, ? 6] enable us to determine the structure of the cohomology algebra H*(S(oo); Z2) by using Borel's theorem on the structure of Hopf ...
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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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