A Remarkable Class of Rings |
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Authors: | Maurizio Iurlo Maria Scafati Tallini |
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Affiliation: | 1. Largo dell’Olgiata 15/106/1C, 00123, Rome, Italy 2. Viale Ippocrate 97, 00161, Rome, Italy
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Abstract: | We consider a remarkable class of rings, which we call corpids, that is the rings (K, +, ·), such that (K, ·) is an inverse semigroup (or groupid, which is the name used by Tallini (Ann Math 71:295–322, 1966). 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. |
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