They are not called b-g algae anymore, they have been reclassified as cyanobacteria.
B-g algae, monera, all that taxaonomy was based on morphological similarities, which ended up not representing accurate rankings of evolutionary relatedness. Thanks to convergent evolution, two lineages can independently evolve similar traits--succulents of South Africa and cacti from North America look very similar but have not shared a common ancestor for 10s of millions of years (as shown by molecular and fossil evidence).
Cyanobacteria look like algae (only in the gross sense that they are green and "pretty" small), but only share photosynthetic capacity because of the endosymbiotic event. Yup a single celled Eukaryote once ate a cyano, and some how the cyano just ended up living inside the Euk, eventually evolving though time into chloroplasts (which still have remnants the cyanobacterial genome in it).
I hope you guys aren't still using the 5 kingdoms system around here?
