Abstract
A subset {a i}i∈I of non-zero elements of a complete lattice L (with 0) is called independent if for every i ∈ I the equality \( {a_i} \wedge \left( {\mathop V\limits_{j \ne i,j \in I} {a_j}} \right) = 0 \) holds. In this case we use the notation \( \mathop \oplus \limits_{i \in I} {a_i} = \mathop V\limits_{i \in I} {a_i} \) and we call this join a direct sum.
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© 2000 Springer Science+Business Media Dordrecht
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Călugăreanu, G. (2000). Independence. Semiatomic lattices. In: Lattice Concepts of Module Theory. Springer Texts in the Mathematical Sciences, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9588-9_6
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DOI: https://doi.org/10.1007/978-94-015-9588-9_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5530-9
Online ISBN: 978-94-015-9588-9
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