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Isomorphism Theorems on Quasi Module

Abstract

A quasimodel is an algebraic axiomatisation of the hyperspace structure based on a module. We initiated this structure in our paper [2]. It is a generalisation of the module structure in the sense that every module can be embedded into a quasi module and every quasi module contains a module. The structure a quasimodel is a conglomeration of a commutative semigroup with an external ring multiplication and a compatible partial order. In the entire structure partial order has an intrinsic effect and plays a key role in any development of the theory of quasi module. In the present paper we have discussed order-morphism which is a morphism like concept. Also with the help of the quotient structure of a quasi module by means of a suitable compatible congruence, we have proved order-isomorphism theorem.

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A Note on the Uniqueness of Stable Marriage Matching

References [1] E. Drgas-Burchardt and Z. Świtalski, A number of stable matchings in models of the Gale-Shapley type, manuscript. [2] J. Eeckhout, On the uniqueness of stable marriage matchings, Econom. Lett. 69 (2000) 1-8. doi:10.1016/S0165-1765(00)00263-9 [3] D. Gale, The two-sided matching problem: origin, development and current issues, Int. Game Theory Rev. 3 (2001) 237-252. doi:10.1142/S0219198901000373 [4] D. Gale and L.S. Shapley, College admissions and the stability of marriage

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On Closed Modular Colorings of Trees

. Zhang, On closed modular colorings of regular graphs, Bull. Inst. Combin. Appl. 66 (2012) 7-32. [5] G. Chartrand, L. Lesniak and P. Zhang, Graphs & Digraphs, 5th Edition (Chapman & Hall/CRC, Boca Raton, 2010). [6] G. Chartrand and P. Zhang, Chromatic Graph Theory (Chapman & Hall/CRC, Boca Raton, 2008). doi:10.1201/9781584888017 [7] H. Escuadro, F. Okamoto and P. Zhang, Vertex-distinguishing colorings of graphs- A survey of recent developments, AKCE Int. J. Graphs Comb. 4 (2007) 277-299. [8] J.A. Gallian

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On Minimal Geodetic Domination in Graphs

numbers, Opuscula Math. 24 (2004)) 181-188. [13] J. Bondy and G. Fan, A sufficient condition for dominating cycles, Discrete Math. 67 (1987) 205-208. doi:10.1016/0012-365X(87)90029-X [14] E. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Net- works 7 (1977) 247-261. doi:10.1002/net.3230070305 [15] H. Walikar, B. Acharya and E. Samathkumar, Recent Developments in the Theory of Domination in Graphs (Allahabad, 1979). [16] T.L. Tacbobo, F.P.Jamil and S. Canoy Jr., Monophonic and

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Regularity and Planarity of Token Graphs

Mathematics Software (Version 6.8), The Sage Development Team, 2015. http://www.sagemath.org . [13] K. Wagner, Über eine Eigenschaft der ebenen Komplexe , Math. Ann. 114 (1937) 570–590. doi:10.1007/BF01594196

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Per-Spectral Characterizations Of Some Bipartite Graphs

Commun. Math. Comput. Chem. 51 (2004) 137-148. [8] Q. Chou, H. Liang and F. Bai, Computing the permanental polynomial of the high level fullerene C70 with high precision, MATCH Commun. Math. Comput. Chem. 73 (2015) 327-336. [9] E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003) 241-272. doi: 10.1016/S0024-3795(03)00483-X [10] E.R. van Dam and W.H. Haemers, Developments on spectral characterizations of graphs, Discrete Math. 309 (2009) 576-586. doi: 10.1016/j

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Nondistributive Rings and Their Öre Localizations

R eferences [1] K.L. Chew and G.H. Chan, On extensions of near-rings , Nanta Math. 5 (1971) 12–21. [2] J.R. Clay, Nearrings, geneses and applications (Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1992). [3] C.C. Ferrero and G. Ferrero, Nearrings, some developments linked to semigroups and groups (Advances in Mathematics (Dordrecht) 4, Kluwer Academic Publishers, Dordrecht, 2002). [4] L.E. Dickson, Definitions of a group and a field by independent postulates , Trans. Amer. Math. Soc. 6 (1905

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Notes on the Distribution of Roots Modulo a Prime of a Polynomial

References [1] DUKE, W.-FRIEDLANDER, J.B.-IWANIEC, H.: Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. (2) 141 (1995), no. 2, 423-441. [2] HADANO, T.-KITAOKA, Y.-KUBOTA, T.-NOZAKI, M.: Densities of sets of primes related to decimal expansion of rational numbers. (W. Zhang and Y. Tanigawa, eds.) In: Number Theory: Tradition and Modernization, The 3rd China-Japan seminar on number theory, Xi’an, China, February 12-16, 2004. Developments. Math. Vol. 15, 2006, Springer, New York, pp. 67

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