Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathfrak{X}$-elements in multiplicative lattices -- A generalization
  of $J$-ideals, $n$-ideals and $r$-ideals in rings   In this paper, we introduce a concept of $\mathfrak{X}$-element with respect
to an $M$-closed set $\mathfrak{X}$ in multiplicative lattices and study
properties of $\mathfrak{X}$-elements. For a particular $M$-closed subset
$\mathfrak{X}$, we define the concept of $r$-element, $n$-element and
$J$-element. These elements generalize the notion of $r$-ideals, $n$-ideals and
$J$-ideals of a commutative ring with unity to multiplicative lattices. In
fact, we prove that an ideal $I$ of a commutative ring $R$ with unity is a
$n$-ideal ($J$-ideal) of $R$ if and only if it is an $n$-element ($J$-element)
of $Id(R)$, the ideal lattice of $R$.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th