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Year 2020, Volume: 1 Issue: 2, 49 - 62, 30.07.2020

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References

  • Bishop E., Foundations of Constructive Analysis, McGraw-Hill, 1967.
  • Bishop E., Bridges D.S., Constructive Analysis, Grundlehren der Mathematischen Wissenschaften 279, Springer, 1985.
  • Bonzio S., Algebraic Structures from Quantum and Fuzzy Logics, Ph.D. Thesis. Universit`a degli studi di Cagliari, 2015.
  • Bonzio S., Chajda I., Residuated relational systems, Asian-European Journal of Mathematics, 11(2), 1850024, 2018.
  • Bridges D.S., Richman R., Varieties of Constructive Mathematics, London Mathematical Society Lecture Notes, No. 97, Cambridge University Press, 1987.
  • Mines R., Richman F., Ruitenburg W., A Course of Constructive Algebra, Springer, 1988.
  • Romano D.A., Rings and fields, a constructive view, Mathematical Logic Quarterly (MLQ), 34(1), 25-40, 1988.
  • Romano D.A., Coequality relations, a survey, Bulletin of the Society of Mathematicians Banja Luka, 3, 1-36, 1996.
  • Romano D.A., The second isomorphism theorem on ordered set under antiorders, Kragujevac Journal of Mathematics, 30, 235-242, 2007.
  • Romano D.A., A note on quasi-antiorder in semigroup, Novi Sad Journal of Mathematics, 37(1), 3-8, 2007.
  • Romano D.A., Co-ideals and co-filters in ordered set under co-quasiorder, Bulletin of the International Mathematical Virtual Institute, 8(1), 177-188, 2018.
  • Romano D.A., Some algebraic structures with apartness, a review, Journal of the International Mathematical Virtual Institute, 9(2), 361-395, 2019.
  • Romano D.A., Co-quasiordered residuated systems, an introduction, Asian-European Journal of Mathematics, 12(5), 1950073, 2019.
  • Romano D.A., On co-filters in co-quasiordered residuated system, Ikonion Journal of Mathematics, 1(2), 27-33, 2019.
  • Troelstra A.S., van Dalen D., Constructivism in Mathematics: An Introduction, North-Holland, 1988.

Two Types of Quotient Structure of Co-Quasiordered Residuated Systems

Year 2020, Volume: 1 Issue: 2, 49 - 62, 30.07.2020

Abstract

In our article we introduced and analysed the concept of residuated relational systems ordered under co-quasiorder. In this article, as a continuation of the mentioned paper, we introduce two types of quotient structures of residuated relational systems are constructed, one of which is a specificity of Bishop's constructive framework and has no counterpart in the classical theory. The paper finished by a theorem which can be viewed as the first isomorphism theorem for these algebraic structures.

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Thanks

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References

  • Bishop E., Foundations of Constructive Analysis, McGraw-Hill, 1967.
  • Bishop E., Bridges D.S., Constructive Analysis, Grundlehren der Mathematischen Wissenschaften 279, Springer, 1985.
  • Bonzio S., Algebraic Structures from Quantum and Fuzzy Logics, Ph.D. Thesis. Universit`a degli studi di Cagliari, 2015.
  • Bonzio S., Chajda I., Residuated relational systems, Asian-European Journal of Mathematics, 11(2), 1850024, 2018.
  • Bridges D.S., Richman R., Varieties of Constructive Mathematics, London Mathematical Society Lecture Notes, No. 97, Cambridge University Press, 1987.
  • Mines R., Richman F., Ruitenburg W., A Course of Constructive Algebra, Springer, 1988.
  • Romano D.A., Rings and fields, a constructive view, Mathematical Logic Quarterly (MLQ), 34(1), 25-40, 1988.
  • Romano D.A., Coequality relations, a survey, Bulletin of the Society of Mathematicians Banja Luka, 3, 1-36, 1996.
  • Romano D.A., The second isomorphism theorem on ordered set under antiorders, Kragujevac Journal of Mathematics, 30, 235-242, 2007.
  • Romano D.A., A note on quasi-antiorder in semigroup, Novi Sad Journal of Mathematics, 37(1), 3-8, 2007.
  • Romano D.A., Co-ideals and co-filters in ordered set under co-quasiorder, Bulletin of the International Mathematical Virtual Institute, 8(1), 177-188, 2018.
  • Romano D.A., Some algebraic structures with apartness, a review, Journal of the International Mathematical Virtual Institute, 9(2), 361-395, 2019.
  • Romano D.A., Co-quasiordered residuated systems, an introduction, Asian-European Journal of Mathematics, 12(5), 1950073, 2019.
  • Romano D.A., On co-filters in co-quasiordered residuated system, Ikonion Journal of Mathematics, 1(2), 27-33, 2019.
  • Troelstra A.S., van Dalen D., Constructivism in Mathematics: An Introduction, North-Holland, 1988.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Daniel A. Romano

Project Number -
Publication Date July 30, 2020
Published in Issue Year 2020 Volume: 1 Issue: 2

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.