On co-filters in co-quasiordered residuated system

Yıl 2019, Cilt: 1 Sayı: 2, 27 - 33, 16.10.2019

Daniel A. Romano

Öz

Residuated relational systems have been the focus of many researchers in the past decade.
In this article, as a continuation of \cite{Rom19a}, we focused on residuated relational systems $\langle A,\cdot,\rightarrow,1,\nprec \rangle$ ordered under co-quasiorder relation $'\nprec\,'$ within the Bishop's constructivist framework.
In this report we we give some new results on co-filters in such relational systems by more depth and deeper analyzing of the connection between the internal operation $'\cdot\,'$ and $'\rightarrow\,'$ with the co-quasiorder relation.

Anahtar Kelimeler

Bishop's constructive mathematics, set with apartness, co-quasiordered residuated system, co-filter

Kaynakça

• E. Bishop. Foundations of Constructive Analysis, New York: McGraw-Hill, 1967.
• E. Bishop and D. S. Bridges. Constructive Analysis, Grundlehren der mathematischen Wissenschaften 279, Berlin: Springer, 1985.
• S. Bonzio. Algebraic structures from quantum and fuzzy logics. Ph.D Thesis. Cagliari: Universit`a degli studi di Cagliari, 2015.
• S. Bonzio and I. Chajda. Residuated relational systems. Asian-European J. Math., 11(2)(2018) 1850024
• D. S. Bridges and F. Richman. Varieties of Constructive Mathematics, Cambridge: London Mathematical Society Lecture Notes, No. 97,Cambridge University Press, 1987.
• R. Mines, F. Richman and W. Ruitenburg. \emph{A Course of constructive algebra}. New York: Springer, 1988.
• D. A. Romano. Co-ideals and co-filters in ordered set under co-quasiorder. Bull. Int. Math. Virtual Inst., 8(1)(2018), 177--188.
• D. A. Romano. Some algebraic structures with apartness, A review. J. Int. Math. Virtual Inst., 9(2)(2019), 361--395.
• D. A. Romano. Co-quasiordered residuated systems, An introduction. Asian-European J. Math., 12(5)(2019) ID 1950073
• D. A. Romano. Co-ideals in a residuated relational system ordered under a co-quasiorder. Available at https://www.researchgate.net/profile/Daniel Romano
• D. A. Romano. Filters in residuated relational system ordered under quasi-order. Available at https://www.researchgate.net/profile/Daniel Romano
• D. A. Romano. Ideals in quasi-ordered residuated system. Available at https://www.researchgate.net/profile/Daniel Romano\bibitem{Troelstra} A. S. Troelstra and D. van Dalen. \emph{Constructivism in Mathematics: An Introduction}, Amsterdam: North-Holland, 1988.