Statisch pairs in atomistic posets

Alireza Vaezi; Vilas Kharat

Mathematica Bohemica (2017)

  • Volume: 142, Issue: 2, page 125-136
  • ISSN: 0862-7959

Abstract

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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. ∇ -relation is partly studied by means of statisch pairs.

How to cite

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Vaezi, Alireza, and Kharat, Vilas. "Statisch pairs in atomistic posets." Mathematica Bohemica 142.2 (2017): 125-136. <http://eudml.org/doc/288104>.

@article{Vaezi2017,
abstract = {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.},
author = {Vaezi, Alireza, Kharat, Vilas},
journal = {Mathematica Bohemica},
keywords = {atomistic poset; statisch pair; finite element},
language = {eng},
number = {2},
pages = {125-136},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Statisch pairs in atomistic posets},
url = {http://eudml.org/doc/288104},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Vaezi, Alireza
AU - Kharat, Vilas
TI - Statisch pairs in atomistic posets
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 2
SP - 125
EP - 136
AB - 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.
LA - eng
KW - atomistic poset; statisch pair; finite element
UR - http://eudml.org/doc/288104
ER -

References

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  2. Janowitz, M. F., 10.4064/fm-89-3-225-227, Fundam. Math. 89 225-227 (1975). (1975) Zbl0321.06009MR0382095DOI10.4064/fm-89-3-225-227
  3. Maeda, F., Maeda, S., 10.1007/978-3-642-46248-1, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 173. Springer, Berlin (1970). (1970) Zbl0219.06002MR0282889DOI10.1007/978-3-642-46248-1
  4. Shewale, R. S., Modular Pairs, Forbidden Configurations and Related Aspects in Partially Ordered Sets, Ph. D. Thesis, University of Pune, Pune (INDIA) (2010). (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). (2003) Zbl1117.06300MR2290805
  6. Vaezi, A., Kharat, V., 10.22436/jmcs.016.01.07, J. Math. Computer Sci. (electronic only) 1 (2016), 69-76. Avaible at http://www.isr-publications.com/jmcs/volume-16/issue-1. (2016) DOI10.22436/jmcs.016.01.07
  7. Waphare, B. N., Symmetricity in Posets, Comparability Axioms in Orthomodular Lattices with Applications, Ph. D. Thesis, University of Pune, Pune, India (1992). (1992) 
  8. Waphare, B. N., Joshi, V. V., Distributive pairs in biatomic lattices, Acta. Math. Univ. Comen., New Ser. 73 (2004), 69-73. (2004) Zbl1094.06007MR2076044
  9. Waphare, B. N., Joshi, V. V., Biatomic pairs in posets, Southeast Asian Bull. Math. 31 (2007), 789-800. (2007) Zbl1150.06005MR2363032
  10. Waphare, B. N., Joshi, V. V., Distributive pairs in posets, Southeast Asian Bull. Math. 31 (2007), 1205-1233. (2007) Zbl1150.06006MR2386998
  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. (1996) Zbl0842.06004
  12. Wille, R., 10.1007/BF01111258, Math. Z. 94 (1966), 1-31. (1966) Zbl0144.00704MR0216989DOI10.1007/BF01111258

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