Geodesic
Statisch pairs in atomistic posets
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 125-136
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We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. $\nabla $-relation is partly studied by means of statisch pairs.
We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal. $\nabla $-relation is partly studied by means of statisch pairs.
DOI : 10.21136/MB.2016.0076-13
Classification : 06A06, 06A11
Keywords: atomistic poset; statisch pair; finite element 
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Vaezi, Alireza; Kharat, Vilas. Statisch pairs in atomistic posets. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 125-136. doi: 10.21136/MB.2016.0076-13

[1] Janowitz, M. F.: On the modular relation in atomistic lattices. Fundam. Math. 66 (1970), 337-346. | DOI | MR | JFM

[2] Janowitz, M. F.: Examples of statisch and finite statisch AC-lattices. Fundam. Math. 89 225-227 (1975). | DOI | MR | JFM

[3] Maeda, F., Maeda, S.: Theory of Symmetric Lattices. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 173. Springer, Berlin (1970). | DOI | MR | JFM

[4] Shewale, R. S.: Modular Pairs, Forbidden Configurations and Related Aspects in Partially Ordered Sets. Ph. D. Thesis, University of Pune, Pune (INDIA) (2010).

[5] Thakare, N. K., Maeda, S., Waphare, B. N.: Modular pairs, covering property and related results in posets. J. Indian Math. Soc. (N.S.) 70 229-253 (2003). | MR | JFM

[6] Vaezi, A., Kharat, V.: Completeness and compact generation in partially ordered sets. J. Math. Computer Sci. (electronic only) 1 (2016), 69-76. Avaible at http://www.isr-publications.com/jmcs/volume-16/issue-1 | DOI

[7] Waphare, B. N.: Symmetricity in Posets, Comparability Axioms in Orthomodular Lattices with Applications. Ph. D. Thesis, University of Pune, Pune, India (1992).

[8] Waphare, B. N., Joshi, V. V.: Distributive pairs in biatomic lattices. Acta. Math. Univ. Comen., New Ser. 73 (2004), 69-73. | MR | JFM

[9] Waphare, B. N., Joshi, V. V.: Biatomic pairs in posets. Southeast Asian Bull. Math. 31 (2007), 789-800. | MR | JFM

[10] Waphare, B. N., Joshi, V. V.: Distributive pairs in posets. Southeast Asian Bull. Math. 31 (2007), 1205-1233. | MR | JFM

[11] Wasadikar, M. P., Thakare, N. K.: $p$-elements and statisch pairs in lattices. Publ. Cent. Rech. Math. Pures Sér. I 27 (1996), 1-5. | JFM

[12] Wille, R.: Halbkomplementäre Verbände. Math. Z. 94 (1966), 1-31. | DOI | MR | JFM

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