On Regular Rings.

@article{vonNeumann1936OnRR,
  title={On Regular Rings.},
  author={John von Neumann},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1936},
  volume={22 12},
  pages={
          707-13
        }
}
  • J. von Neumann
  • Published 1936
  • Mathematics
  • Proceedings of the National Academy of Sciences of the United States of America
Continuous geometry is a complete complemented irreducible modular lattice in which join and meet are continuous. Von Neumann invented Regular Rings in order to " Coordinise " these lattices. In this chapter we present the basic properties of general regular rings, the nature and use of idempotents, the class of all principal right ideals (left ideals) as a complemented modular lattice, and other general properties of regular rings which are useful in the remaining chapters. 
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183 Citations

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