# 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 } }

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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