On co-Filters in Semigroups with Apartness
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Authors: D. A. ROMANO
DOI: 10.46793/KgJMat2104.607R
Abstract:
The logical environment of this research is the Intuitionistic Logic and principled-philosophical orientation of the Bishop’s Constructive Mathematics. In this paper, basing our consideration on the sets with the apartness relation, we analyze the lattices of all co-filters of an ordered semigroup under a co-quasiorder as a continuation of our article [?]. We prove a number of results related to co-filters in a semigroup with apartness and the lattice of all co-filters of such semigroups.
Keywords:
Bishop’s constructive mathematics, semigroup with apartness, co-order and co-quasiorder relations, co-filters.
References:
[1] C. E. Aull, Ideals and filters, Compos. Math. 18(1-2) (1967), 79–86.
[2] E. Bishop, Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.
[3] E. Bishop and D. Bridges, Constructive Analysis, Grundlehren der Mathematischen Wissenschaften 279, Springer, Berlin, 1985.
[4] D. Bridges and F. Richman, Varieties of Constructive Mathematics, London Mathematical Society Lecture Notes 97, Cambridge University Press, Cambridge, 1987.
[5] D. S. Bridges and L. S. Vita, Apartness and Uniformity: A Constructive Development, CiE series - Theory and Applications of Computability, Springer Verlag, Berlin, Heidelberg, 2011.
[6] S. Crvenković, M. Mitrović and D. A. Romano, Semigroups with Apartness, Mathematical Logic 59(6) (2013), 407–414.
[7] S. Crvenković, M. Mitrović and D. A. Romano, Basic notions of (constructive) semigroups with apartness, Semigroup Forum 92(3) (2016), 659–674.
[8] O. Frink and R. S. Smith, On the distributivity of the lattice of filters of a groupoid, Pac. J. Math. Ind. 42 (1972), 313–322.
[9] J. Jakubak, On filters of ordered semigroups, Czechoslovak Math. J. 43(3) (1993), 519–522.
[10] Z. Juhasz and A. Vernitski, Filters in (quasiordered) semigroups and lattices of filters, Communication in Algebra 39(11) (2011), 4319–4335.
[11] R. Mines, F. Richman and W. Ruitenburg, A Course of Constructive Algebra, Springer, New York, 1988.
[12] M. Mitrović, S. Crvenković and D. A. Romano, Semigroups with apartness: constructive versions of some classical theorems, in: Proceedings of The 46th Annual Iranian Mathematics Conference, 25-28 August 2015, Yazd University, Yazd, Iran, 2016, 64–67.
[13] M. S. Rao and A. El-M. Badawy, Filters of lattices with respect to a congruence, Discuss. Math. Gen. Algebra Appl. 34(2014), 213–219.
[14] D. A. Romano, A note on a family of quasi-antiorder on semigroup, Kragujevac J. Math. 27 (2005), 11–18.
[15] D. A. Romano, The second isomorphism theorem on ordered set under anti-orders, Kragujevac J. Math. 30 (2007), 235–242.
[16] D. A. Romano, A note on quasi-antiorder in semigroup, Novi Sad J. Math. 37(1) (2007), 3–8.
[17] D. A. Romano, An isomorphism theorem for anti-ordered sets, Filomat 22(1) (2008), 145–160.
[18] D. A. Romano, On quasi-antiorder relation on semigroups, Mat. Vesnik 64(3) (2012), 190–199.
[19] D. A. Romano, Co-ideals and co-filters in ordered set under co-quasiorder, Bull. Int. Math. Virtual Inst. 8(1) (2018), 177–188.
[20] A. Troelstra and D. van Dalen, Constructivism in Mathematics, An Introduction, Volume II, North-Holland, Amsterdam, 1988.
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