Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

Dudzik, Dariusz; Skrzynski, Marcin

doi:10.1515/amsil-2016-0020

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Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

Annales Mathematicae Silesianae

Volume 31 (2017): Issue 1 (September 2017)

By: Dariusz Dudzik and Marcin Skrzynski

Open Access

|Sep 2017

Abstract

On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.

References

[1] Atiyah M.F., MacDonald I.G., Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Reading, 1969.
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[2] Dudzik D., Skrzynski M., An outer measure on a commutative ring, Algebra Discrete Math. 21 (2016), no. 1, 51-58.
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[3] Federer H., Geometric Measure Theory, Springer, Berlin, 1969.
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[4] Halmos P.R., Measure Theory, Springer, New York, 1976.
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DOI: https://doi.org/10.1515/amsil-2016-0020 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 63 - 70

Submitted on: Aug 3, 2016

Accepted on: Nov 18, 2016

Published on: Sep 13, 2017

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

outer measure,

commutative ring,

prime ideal,

Carathéodory’s condition,

ring of functions,

unique factorization domain

Related subjects:

Mathematics,

General mathematics

© 2017 Dariusz Dudzik, Marcin Skrzynski, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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