Abstract
The aim of our paper is twofold. First, we thoroughly study the set of meager elements $$\hbox{M}(E),$$ the center $$\hbox{C}(E)$$ and the compatibility center $$\hbox{B}(E)$$ in the setting of atomic Archimedean lattice effect algebras $$E.$$ The main result is that in this case the center $$\hbox{C}(E)$$ is bifull (atomic) iff the compatibility center $$\hbox{B}(E)$$ is bifull (atomic) whenever $$E$$ is sharply dominating. As a by-product, we give a new description of the smallest sharp element over $$x\in E$$ via the basic decomposition of $$x.$$ Second, we prove the Triple Representation Theorem for sharply dominating atomic Archimedean lattice effect algebras.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
