# Algebraic ramifications of the common extension problem for group-valued measures

Fundamenta Mathematicae (1994)

- Volume: 146, Issue: 1, page 1-20
- ISSN: 0016-2736

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topGöbel, Rüdiger, and Shortt, R.. "Algebraic ramifications of the common extension problem for group-valued measures." Fundamenta Mathematicae 146.1 (1994): 1-20. <http://eudml.org/doc/212048>.

@article{Göbel1994,

abstract = {Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.},

author = {Göbel, Rüdiger, Shortt, R.},

journal = {Fundamenta Mathematicae},

keywords = {field of sets; Stone space; charge; common extension; Abelian group; independence},

language = {eng},

number = {1},

pages = {1-20},

title = {Algebraic ramifications of the common extension problem for group-valued measures},

url = {http://eudml.org/doc/212048},

volume = {146},

year = {1994},

}

TY - JOUR

AU - Göbel, Rüdiger

AU - Shortt, R.

TI - Algebraic ramifications of the common extension problem for group-valued measures

JO - Fundamenta Mathematicae

PY - 1994

VL - 146

IS - 1

SP - 1

EP - 20

AB - Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

LA - eng

KW - field of sets; Stone space; charge; common extension; Abelian group; independence

UR - http://eudml.org/doc/212048

ER -

## References

top- [1] A. Basile and K. P. S. Bhaskara Rao, Common extensions of group-valued charges, Boll. Un. Mat. Ital. 7 (5-A) (1991), 157-162. Zbl0741.28008
- [2] A. Basile, K. P. S. Bhaskara Rao and R. M. Shortt, Bounded common extensions of bounded charges, Proc. Amer. Math. Soc. 121 (1994), 137-143. Zbl0807.28002
- [3] K. P. S. Bhaskara Rao and R. M. Shortt, Common extensions for homomorphisms and group-valued charges, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 125-140. Zbl0777.28005
- [4] K. P. S. Bhaskara Rao and R. M. Shortt, Group-valued charges: common extensions and the finite Chinese remainder property, Proc. Amer. Math. Soc. 113 (1991), 965-972. Zbl0743.28004
- [5] T. Carlson and K. Prikry, Ranges of signed measures, Period. Math. Hungar. 13 (1982), 151-155. Zbl0523.28003
- [6] S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235. Zbl0138.01801
- [7] L. Fuchs, Infinite Abelian Groups, Vols. I and II, Academic Press, New York, 1970 & 1973.
- [8] R. Göbel and R. Prelle, Solution of two problems on cotorsion abelian groups, Arch. Math. (Basel) 31 (1978), 423-431. Zbl0387.20040
- [9] Z. Lipecki, On common extensions of two quasi-measures, Czechoslovak Math. J. 36 (1986), 489-494. Zbl0622.28007
- [10] E. Marczewski, Measures in almost independent fields, Fund. Math. 38 (1951), 217-229. Zbl0045.02303
- [11] K. M. Rangaswamy and J. D. Reid, Common extensions of finitely additive measures and a characterization of cotorsion Abelian groups, in: Proc. Curacao, Abelian Groups, Marcel Dekker, New York, 1993, 231-238. Zbl0817.20056
- [12] L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), 11-32.

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