# modular lattice

## modular lattice

(mathematics)
A lattice with the property that, if x is equal to or greater than z, then for any element y, the greatest lower bound of x and v equals the least upper bound of w and z, where v is the least upper bound of y and z and w is the greatest lower bound of x and y.
References in periodicals archive ?
The Miche system is a modular lattice system capable of arbitrary shape formation.
5] Every distributive lattice is a modular lattice.
Let L be a modular lattice and D be a generalized f-derivation on L where f : L [right arrow] L is a join-homomorphism.
It is known  that if there exists a positive valuation v on L, then L must be a modular lattice.
The concept of modular lattice, distributive lattice, super modular lattice and chain lattices can be had from .
5 has a sublattice which is a modular pure neutrosophic lattice and sublattice which is a usual modular lattice.
5 is not distributive as it contains sublattices whose homomorphic image is isomorphic to the neutrosophic modular lattice N([M.
So we define a neutrosophic lattice N(L) to be a quasi modular lattice if it has atleast one sublattice (usual) which is modular and one sublattice which is a pure neutrosophic modular lattice.
In case of edge neutrosophic lattices, we can have edge neutrosophic distributive lattices, edge neutrosophic modular lattices and edge neutrosophic super modular lattices and so on.
Vasantha, On a certain class of Modular lattices, J.
Vasantha Kandasamy and Florentin Smarandache, Super modular Lattices, Educational Publisher, Ohio, 2012.
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