Homological Algebra in Locally Compact Abelian Groups

Moskowitz, Martin

doi:10.2307/1994421

Cited by 20 publications

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“…2], (P, H) = (H)1, where H denotes the character group of H and (P, H) the annihilator of P in H. Hence (H/P)^ = (H)1. Since (HjP)^ is connected, HjP is torsion free as can be argued from the abelian theory [12]. Thus G/P^ W'x D, where D = H\P has the requisite properties.…”

Section: Corollarymentioning

confidence: 93%

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On Central Topological Groups

Grosser¹,

Moskowitz²

1967

Transactions of the American Mathematical Society

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Section: Corollarymentioning

confidence: 93%

“…Math. 81 (1957); see also [12]. On the direct product NxZ we define a continuous homomorphism <j>3: N x Z -^-V by <f>3(x, f ) = cf>(x) + <f>2(z).…”

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confidence: 99%

On Central Topological Groups

Grosser¹,

Moskowitz²

1967

Transactions of the American Mathematical Society

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“…Therefore the character group of a compactly generated object of i£ is isomorphic with a group of the form Tm © Rn © D, where £ is a discrete abelian group. A group of this form is called a group without small subgroups (see [7]). We know that any object of if is a proper inductive limit of its compactly generated open subgroups.…”

Section: Qedmentioning

confidence: 99%

Functorial Characterizations of Pontryagin Duality

Roeder¹

1971

Transactions of the American Mathematical Society

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“…The reader may wish to contrast our work with that of M. Moskowitz in the category EE of locally compact abelian groups [9]. J. Dixmier [3] and P. R. Ahern and R. I. Jewett [1] independently characterized the injectives in EE as groups of the form £" x T", where £ is the additive group of real numbers, £is the circle group, n is finite, and a is an arbitrary cardinal number.…”

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confidence: 99%

The projective dimension of a compact abelian group

Nummela¹

1973

Proc. Amer. Math. Soc.

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Abstract.Let A" be a compact group, FGX the (Graev) free topological group generated by X, and K the kernel of the canonical quotient morphism from FGX to X. Then A" is a (Graev) free topological group. A corollary to the abelian analogue of this theorem is that the projective dimension of a compact abelian group, relative to the class of all continuous epimorphisms admitting sections, is exactly one. Introduction.Let 'S (respectively, s/) denote the category of topological (abelian) groups and continuous group homomorphisms. We take as known the definitions and elementary properties of topological groups as presented in, for example, [2, pp. 219-250]. We adopt the convention that all groups are topological, using the modifier "algebraic" for those groups without topologies. Moreover, all our topologies satisfy the Hausdorff separation axiom.We assume also some familiarity with the notions of free (topological) groups due to A. A. Markov [8] and M. I. Graev [5]. Given a completely regular space X, we denote by FX (ZX) the Markov free (free abelian) group over X, and by FGX (ZGX) the Graev free (free abelian) group over X. Recall that if A' is a compact space, then FGX is the colimit of the expanding sequence {Fm} of compact spaces, where Fm is the set of all words in FGX whose reduced length relative to X\{e} is less than or equal to m (e is the identity of FGX). An analogous result holds for FX, ZGX, and ZX.Recall that a group P in 'S (s/) is projective relative to a class S of epimorphisms in 'S (stf) if, given any diagram P I

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Homological Algebra in Locally Compact Abelian Groups

Cited by 20 publications

References 0 publications

On Central Topological Groups

On Central Topological Groups

Functorial Characterizations of Pontryagin Duality

The projective dimension of a compact abelian group

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