Τίτλος:
Divisorial elements in lattice-ordered monoids
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
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.
Συγγραφείς:
Fuchs, L
Kehayopulu, N
Reis, R
Tsingelis, M
Περιοδικό:
Semigroup Forum
DOI:
10.1007/s00233-004-0163-8