Some Characterizations and sheaf representations of regular and weakly regular monoids and semirings

Abstract

A ring R is called regular it for each a E R, there exists an element X E R such that axa=a. Regular rings were introduced by von Neumann in 1936, in order to clarify certain aspects of operator algebras. Since then regular rings have been very extensively studied both for their own sake, as well as for the sake of their links with operator algebras. .......................