Quasi-modular Pseudo-Complemented Semi-lattices

Main Article Content

Sanaa El Assar M. Atallah E. Atef

Abstract

In this paper we dene and introduce a new class of pseudocomplemented semilattices ; the class of quasi-modular pseudocomplemented semilattices; which generalizes modular pseudocomplemented semilattices.We give a characterization and a construction of such class, using a triple containing a Boolean algebra, a semilattice with a greatest element and a structure map. We describe homomorphisms, subalgebras and congruencerelations of the quasi-modular pseudo-complemented semi-lattices by means of triples.

Article Details

How to Cite
El Assar, S., Atallah, M., & Atef, E. (2016). Quasi-modular Pseudo-Complemented Semi-lattices. Acta Mathematica Universitatis Comenianae, 85(2), 173-180. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/126/383
Section
Articles

References

[1] I. Chajda, R. Halas and J. Kuhr, Semilattice Structures, Research and Exposition in Mathematics, V 30,Heldermann Verlag, 2007.

[2] C. C. Chen and G. Gratzer Stone Lattice I, Construction Theorems. Canda. J. Math.21(1969),884-894.

[3] C. C. Chen and G. Gratzer Stone Lattice II, Structure Theorems. Canda. J. Math.21(1969),895-903.

[4] W. Cornish, Pseudo-complemented modular semilattices, J. Austral Math. Soc. 18 (1974), 239-251.

[5] S. El Assar, Two notes of the congreunce lattice of the p-algebras, Acta Math. Univ. comenianae (1985), 13-20

[6] S. El Assar, Ghareeb E., Bi-double Stone Algebras Rough Sets, Information-Tokyo 11 (2008), 5-14.

[7] S. El Assar, Ghareeb E., Pseudocomplemented Bilattices, Information-Tokyo 12 (2009), 5-12.

[8] O. Frink, Pseudo-complements in semilattices, Duke Math. J. Austral Math. Soc. 18 (1974).

[9] V. Glivenko, Sur quelques points de la logique de M. Brouwer, Bull. Acad. des Sci. de Belgique 15 (1929),
183-188.

[10] G. Gratzer, Lattice Theory. First concepts and distributive lattices, W. H. Freeman and Co, 1971.

[11] T. Katrinak, Die freien Stoneschen Verbgmde und ihre Tripelcharakterisierung, Acta Math. Acad. Sci. Hungar. 23 (1972), 315-326.

[12] T. Katrinak, Die Kennzeichnung der beschriinkten Brouwerschen Verbande, Czech. Math. J. 22 (97) (1972),
427-434.

[13] T. Katrinak, A new proof of the Construction Theorem for Stone algebras, Proc. Amer. Math. Soc. 40 (1973), 75-78.

[14] T. Katrinak, Die Kennzeichnungder Distributiven pseudokomplementaren Halbverbande, J. reine angew.
Math. 241 (1970), 160-179.

[15] T. Katrinak, Uber eine Konstruktion der distributiven pseudokomplementaren Verbande, Math Nachr. 53
(1972), 85-99.

[16] T. Katrinak, P. Mederly, Constructions of modular p-algebras, Algebra Univ. 4(1974),301-315.

[17] T. Katrinak, p-algebras, Colloq. Math. Soc. J. Bolyai, Szeged (1980),549-573.

[18] T. Katrinak, P. Mederly, Constructions of p-algebras, Algebra Universalis 17(1983),288-316.

[19] T. Katrinak, S. El Assar, p-algebras with stone congreunce lattices, Acta Sci. Math.(Szeged) 51(1987),
371-386

[20] P. Mederly, A Characterization of modular pseudocomplemented semilattices, Colloq uia Math. Soc. Janos Bolyai (1974),231-248.

[21] P. V. R. Murty and V. V. R. Rao, Characterization of certain classes of pseudo semi-lattices, Algebra Univ.
4 (1974), 298-300.

[22] W.C. Nemitz, Implicative semilattices, Trans. Am. Math. Soc. 117 (1965) 128-142.

[23] J. Schmidt, Quasi-decompositions, exact sequences and triple sums of semigroups. L General theory, Colloq.
Math, Soc. J. Bolyai 17 (1975), 365-397.

[24] J. Schmidt, Quasi-decompositions, exact sequences and triple sums of semigroups. II. Applications, Colloq.
Math. Soc. J. Bolyai 17 (1975), 399-428.