Mathematica Bohemica, Vol. 142, No. 2, pp. 125-136, 2017
Statisch pairs in atomistic posets
Alireza Vaezi, Vilas Kharat
Received November 21, 2013. First published November 24, 2016.
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.
Keywords: atomistic poset; statisch pair; finite element
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Affiliations: Alireza Vaezi, Department of Mathematics, Shahid Rajaee Teacher Training University, Imam Ali Highway, Tehran, 16785-136, Iran, e-mail: firstname.lastname@example.org; Vilas Kharat, Department of Mathematics, Savitribai Phule Pune University, Pune University Road, Ganeshkhind, Pune, Maharastra-411007, India, e-mail: email@example.com