Extension of an almost $f$-algebra multiplication

E. Chil

Institut Préparatoire aux Études d'Ingénieurs de Tunis, Monflery, Tunisia

Abstract: It is proved that an almost $f$-algebra multiplication and a $d$-algebra multiplication defined on a majorizing vector sublattice of a Dedekind complete vector lattice can be extended to the whole vector lattice by using purely algebraic and order theoretical means.

Key words: almost $f$-algebra, $d$-algebra, $f$-algebra, vector lattice.

MSC: 06F25, 46A40

Received: 04.10.2011

Language: English