2023/10/26 by Herrmann, Christian
#06C20 #16E50 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2310.17298
Based on an analogue for systems of partial isomorphisms between lower sections in a complemented modular lattice we prove that principal right ideals aR ≅ bR in a (von Neumann) regular ring R are perspective if aR ∩ bR is of finite height in L(R). This is applied to derive, for existence-varieties V of regular rings, equivalence of unit-regularity and direct finiteness, both conceived as a property shared by all members of V.