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Near approximations in rings

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

This paper is a continuation of ideas presented by Bagirmaz (Appl Algebra Eng Commun Comput 30(4):285–297, 2019). Indeed, we introduce the notion of near approximations in a ring, which is an extended notion of a rough approximations in a ring. Then we define lower and upper near subrings based on ideals in a ring and give some properties of such subrings. Furthermore, we obtain a comparison between these types of approximations and the approximations introduced by Davvaz (Inf Sci 176:2417–2437, 2006).

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Acknowledgements

The paper was essentially prepared during the first author’s stay at the Department of Mathematics, Institut Teknologi Sepuluh Nopember under World Class Professor Program 2019 organized by Ministry of Research, Technology and Higher Education of the Republic of Indonesia. Also, the authors would like to thank the anonymous referees for their constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Yazd University, Yazd, Iran

    Bijan Davvaz

  2. Department of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS, Sukolilo, Surabaya, 60111, Indonesia

    Soleha, Dian Winda Setyawati, Imam Mukhlash &  Rinurwati

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  1. Bijan Davvaz
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  2. Soleha
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  3. Dian Winda Setyawati
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  4. Imam Mukhlash
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  5. Rinurwati
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Correspondence to Bijan Davvaz.

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Davvaz, B., Soleha, Setyawati, D.W. et al. Near approximations in rings. AAECC 32, 701–721 (2021). https://doi.org/10.1007/s00200-020-00421-3

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  • DOI: https://doi.org/10.1007/s00200-020-00421-3

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