Abstract

We consider a remarkable class of rings, which we call corpids, that is the rings (K, +, ·), such that (K, ·) is an inverse semigroup. We prove several theorems concerning this structure, an order relation which allows us to formulate characterization theorems. We define the notion of simple idempotent and prove theorems about zero-divisors, idempotents, subcorpids, ideals and characteristic in a corpid.