Displaying 121 – 140 of 226

Showing per page

On Riesz homomorphisms in unital f -algebras

Elmiloud Chil (2009)

Mathematica Bohemica

The main topic of the first section of this paper is the following theorem: let A be an Archimedean f -algebra with unit element e , and T A A a Riesz homomorphism such that T 2 ( f ) = T ( f T ( e ) ) for all f A . Then every Riesz homomorphism extension T ˜ of T from the Dedekind completion A δ of A into itself satisfies T ˜ 2 ( f ) = T ˜ ( f T ( e ) ) for all f A δ . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion. A second application...

On some interpolation rules for lattice ordered groups

Ján Jakubík (2004)

Czechoslovak Mathematical Journal

Let α be an infinite cardinal. In this paper we define an interpolation rule I R ( α ) for lattice ordered groups. We denote by C ( α ) the class of all lattice ordered groups satisfying I R ( α ) , and prove that C ( α ) is a radical class.

On some types of radical classes

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

Let 𝔪 be an infinite cardinal. We denote by C 𝔪 the collection of all 𝔪 -representable Boolean algebras. Further, let C 𝔪 0 be the collection of all generalized Boolean algebras B such that for each b B , the interval [ 0 , b ] of B belongs to C 𝔪 . In this paper we prove that C 𝔪 0 is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized M V -algebras.

Currently displaying 121 – 140 of 226