Daniel A. ROMANO

Semilattice Co-Congruence in Γ-Semigroups

As a generalization of semigroups, Sen, in 1981, introduced the concept of Γ-semigroups. In theauthor’s paper (D A. Romano. Γ-semigroups with apartness. Bull. Allahabad Math. Soc., 34(1)(2019), 71–83.) itis introduced and analyzed the concept of Γ-semigroups with apartness in Bishop’s constructive framework. In thisarticle, as a continuation of previous research, the concept of co-congruences in Γ-semigroups is introduced andanalyzed. Additionally, it is investigated (co-ordered) semillatice co-congruence on (co-ordered) Γ-semigroup withapartness

PDF

___

[1] Bishop, E., Foundations of Constructive Analysis, New York: McGraw-Hill, 1967. 1, 2.2, 3.7

[2] Bridges, D. S., Richman, F., Varieties of Constructive Mathematics, Cambridge: London Mathematical Society Lecture Notes, No. 97, Cambridge University Press, 1987. 1

[3] Cherubini, A., Frigeri, A., Inverse semigroups with apartness, Semigroup Forum, 98(3)(2019), 571–588. 1, 3

[4] Crvenkovic, S., Mitrovi ´ c, M., Romano, D. A., ´ Semigroups with apartness, Math. Logic Quarterly, 59(6)(2013), 407–414. 1

[5] Crvenkovic, S., Mitrovi ´ c, M., Romano, D. A., ´ Basic notions of (Constructive) semigroups with apartness, Semigroup Forum, 92(3)(2016), 659–674. 1

[6] Hedayati, H., Isomorphisms via congruences on Γ-semigroups and Γ-ideals, Thai J. Math., 11(3)(2013), 563–575. 1

[7] Kehayopulu, N., On ordered Γ-semigroups, Sci. Math. Japonicae Online, e-2010, 37–43. 1, 2.1

[8] Kwon, Y. I. amd Li, S. K., Some special elements in ordered Γ-semigroups. Kyungpook Math. J., 35(3)(1996), 679–685. 1, 2.1

[9] Mines, R., Richman, F. , Ruitenburg, W., A course of constructive algebra, Springer-Verlag, New York 1988. 1

[10] Romano, D. A., Coequality relations, a survey, Bull. Soc. Math. Banja Luka, 3(1996), 1–36. 1, 2.2, 3

[11] Romano, D. A., Co-ideals and co-filters in ordered set under co-quasiorder, Bull. Int. Math. Virtual Inst., 8(1)(2018), 177–188. 2.2

[12] Romano, D. A., Γ-semigroups with apartness, Bull. Allahabad Math. Soc., 34(1)(2019), 71–83. 1, 2.1, 2.4, 2.5, 2.6, 2.7, 3, 3.1

[13] Romano, D. A., Some algebraic structures with apartness. A review, J. Int. Math. Virtual Inst., 9(2)(2019), 361–395. 1, 2.2, 3

[14] Romano, D. A., On coequality relation on set with apartness, Bull. Int. Math. Virtual Inst., 9(1)(2019), 1–9. 2.2, 2.12, 2.13, 3

[15] Romano, D. A., Co-filters in Γ-semigroups ordered under co-order, (To appear) Available at ResearchGate 1, 2.8

[16] Sen, M. K., On Γ-semigroups. In: Proceeding of International Conference on ’Algebra and its Applications,(New Delhi, 1981)’ (pp. 301–308). Lecture Notes in Pure and Appl. Math. 9, New York: Decker Publication, 1984. 1, 2.1

[17] Sen, M. K., Saha, N. K., On Γ-semigroup, I, Bull. Calcutta Math. Soc., 78(1986), 181–186. 1, 2.1

[18] Seth, A. Γ-group congruence on regular Γ-semigroups. Inter. J. Math. Math. Sci., 15(1)(1992), 103–106. 1, 2.1

[19] Siripitukdet, M., Iampan, A., On the least (ordered) semilattice congruence in ordered Γ-semigroups, Thai J. Math., 4(2)(2006), 403–415. 1, 2.1

[20] Troelstra, A. S., van Dalen, D., Constructivism in Mathematics: An Introduction, Amsterdam: North-Holland, 1988. 1