Difference between a boolean algebra and a complete lattice?

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A boolean algebra is a specific type of complemented distributive lattice that also qualifies as a complete lattice. The key distinction lies in the properties of their elements: a boolean algebra includes a zero element (0) and an identity element (1), while a complete lattice ensures that every chain has both minimum and maximum elements. For instance, the powerset of a non-empty set serves as an example of a boolean algebra, where the empty set represents the minimum and the set itself represents the maximum. Both structures share similarities in their lattice properties but differ in their definitions and applications. Understanding these differences is crucial for grasping advanced concepts in lattice theory.
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What is the difference between a boolean algebra and a complete lattice? What are their similarities?
 
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luizgguidi said:
What is the difference between a boolean algebra and a complete lattice? What are their similarities?

a boolean algebra is a complemented distributive lattice. a boolean algebra is a complete lattice. A complemented lattice is one with 'zero element 0 and identity element 1'
while a complete lattice is a lattice in which every chain has a minimum and a maximum elements.
for example, the powerset of an arbitrary non emptyset V is a boolean algebra with minimum element(zero element 0 ) as empty set and maximum element(identity element 1) as V
 

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