TY - JOUR
TI - Divisorial elements in lattice-ordered monoids
AU - Fuchs, L
AU - Kehayopulu, N
AU - Reis, R
AU - Tsingelis, M
JO - Semigroup Forum
PY - 2005
VL - 71
TODO - 2
SP - 188-200
PB - Springer-Verlag
SN - 0037-1912, 1432-2137
TODO - 10.1007/s00233-004-0163-8
TODO - null
TODO - Let S be a commutative lattice-ordered monoid that is conditionally
complete and admits residuals. Imitating the definition of divisorial
ideals in commutative ring theory, we study divisorial elements in S.
The archimedean divisorial elements behave especially nicely. We
establish a Galois correspondence of the divisorial elements in a finite
interval. Assuming the maximum condition on integral divisorial
elements, it is shown that their Krull associated primes are divisorial
and the integral divisorial elements admit irredundant representations
as intersections of finitely many p-components that are p-primal
divisorial elements.
ER -