ISSN:
1420-8911
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For any neutral element a in a bounded latticeL, the mapping x→(x∧,x∨a) representsL as a subdirect product of [0, a]×[a, 1]. It is first shown that for certain neutral elements, the image ofL under this mapping is completely determined by a homomorphism of [0, a] into [a, 1]. Iterating this process, a representation ofL can be obtained as a subdirect product of the intervals [ai, ai+1] for any chain 0=a0〈a1... 〈an〈an+1=1 where each ai is such a neutral element relative to [0, ai+1]. The image in this case is completely determined by a family of homomorphisms πi,j:Ai →Aj(i〈j), where Ai=[ai, ai+1].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01201103
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