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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References
Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroups. Math. Surv. Monogr. no. 7, American mathematical Society (1967)
Preston G.B.: Inverse semi-groups. J. Lond. Math. Soc. 29, 396–403 (1954)
Scafati Tallini M., Iurlo M.: Studio di una classe notevole di anelli dotata di inverso generalizzato. Le Matematiche 63, 39–56 (2008)
Scafati Tallini M., Iurlo M.: Relazione d’ordine in un corpide. Le Matematiche 64, 47–56 (2009)
Scafati Tallini M., Iurlo M.: Corpidi e loro proprietà. Le Matematiche 64, 127–145 (2009)
Tallini G.: Sulla struttura algebrica delle trasformazioni tra parti di un insieme. Ann. Mat. 71, 295–322 (1966)
Vagner V.V.: Generalized groups. Doklady Akad. Nauk SSSR 84, 1119–1122 (1952)
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Iurlo, M., Tallini, M.S. A Remarkable Class of Rings. Results. Math. 57, 163–181 (2010). https://doi.org/10.1007/s00025-009-0007-7
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DOI: https://doi.org/10.1007/s00025-009-0007-7