TL;DR
This paper explores the structure of MV-frames, a class of frame structures associated with complete MV-algebras, including their properties, classifications, and relationships with other algebraic structures.
Contribution
It provides a complete characterization of algebraic and regular MV-frames and investigates nuclei on MV-frames and their connections to Lukasiewicz rings and lattice-ordered groups.
Findings
Characterized algebraic MV-frames
Classified regular MV-frames
Connected MV-frames to lattice-ordered groups
Abstract
Complete MV-algebras are naturally equipped with frame structures. We call them MV-frames and investigate some of their main the properties as frames. We completely characterized algebraic MV-frames as well as regular MV-frames. In addition, we consider nuclei on MV-frames in general and on MV-frames of ideals of Lukasiewicz rings. Finally, we used the Chang-Mundici functor to explore the frame structures of complete unital lattice-ordered groups.
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Taxonomy
TopicsDigital Filter Design and Implementation · Optical Coatings and Gratings · Photonic and Optical Devices