Blue green algae are classified under the kingdom Monera because
The cells have no defined nucleus
The cells have no mitochondria
Blue-green algae or cyanobacteria are photosynthetic bacteria but they are placed under kingdom Monera as they are prokaryotic in nature. They lack membrane bound nucleus and organelles.
Both prokaryotic and eukaryotic cells have cytoplasm. Unicellular eukaryotes are found in kingdom protista.