Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions forcing the existence of relative complements in lattices and
  posets   It is elementary and well-known that if an element x of a bounded modular
lattice L has a complement in L then x has a relative complement in every
interval [a,b] containing x. We show that the relatively strong assumption of
modularity of L can be replaced by a weaker one formulated in the language of
so-called modular triples. We further show that, in general, we need not
suppose that x has a complement in L. By introducing the concept of modular
triples in posets, we extend our results obtained for lattices to posets. It
should be remarked that the notion of a complement can be introduced also in
posets that are not bounded.

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg