maximal lattice
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2019 ◽  
Vol 4 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Berhanu Assaye ◽  
Mihret Alamneh ◽  
Lakshmi Narayan Mishra ◽  
Yeshiwas Mebrat

AbstractIn this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.


2015 ◽  
Vol 154 (1-2) ◽  
pp. 81-111 ◽  
Author(s):  
Gennadiy Averkov ◽  
Amitabh Basu
Keyword(s):  

2012 ◽  
Vol 2013 (16) ◽  
pp. 3722-3731 ◽  
Author(s):  
Jean Raimbault
Keyword(s):  

2011 ◽  
Vol 36 (4) ◽  
pp. 721-742 ◽  
Author(s):  
Gennadiy Averkov ◽  
Christian Wagner ◽  
Robert Weismantel

2010 ◽  
Vol 35 (3) ◽  
pp. 704-720 ◽  
Author(s):  
Amitabh Basu ◽  
Michele Conforti ◽  
Gérard Cornuéjols ◽  
Giacomo Zambelli

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Drew Armstrong

International audience Let $(W,S)$ be an arbitrary Coxeter system. For each sequence $\omega =(\omega_1,\omega_2,\ldots) \in S^{\ast}$ in the generators we define a partial order― called the $\omega \mathsf{-sorting order}$ ―on the set of group elements $W_{\omega} \subseteq W$ that occur as finite subwords of $\omega$ . We show that the $\omega$-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and strong Bruhat orders on the group. Moreover, the $\omega$-sorting order is a "maximal lattice'' in the sense that the addition of any collection of edges from the Bruhat order results in a nonlattice. Along the way we define a class of structures called $\mathsf{supersolvable}$ $\mathsf{antimatroids}$ and we show that these are equivalent to the class of supersolvable join-distributive lattices.


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