Biordered Sets of Regular Rings
Rings and Algebras
2020-10-20 v1
Abstract
The set of idempotents of a regular semigroup is given an abstract characterization as a regular biordered set in [2], and in [4] it is shown how a biordered set can be associated with a complemented modular lattice. Von Neumann has shown earlier that any complemented modular lattice of order greater than 3 can be realized as the lattice of principal right ideals of a regular ring (see [3]). Here we try to connect these ideas to get a characterization of the biordered sets of a class of regular rings.
Cite
@article{arxiv.2010.08931,
title = {Biordered Sets of Regular Rings},
author = {James Alexander and E. Krishnan},
journal= {arXiv preprint arXiv:2010.08931},
year = {2020}
}