On dual semigroups
1960; Springer Nature; Volume: 10; Issue: 2 Linguagem: Inglês
10.21136/cmj.1960.100404
ISSN1572-9141
Autores Tópico(s)semigroups and automata theory
ResumoThe purpose of this paper is to study the structure of a class of so called dual semigroups introduced below.The main results are contai ned in Theorem 2,2, Theorem 3,3, Theorem 4,3 and Theorem 6,1.The notion of a dual ring was introduced by R. BAER [2], I. KAPLANSKY [6] and further developped by F. F. BONSALL and A. W. GOLDIE [3] and K. G. WOLFSON [13].The first step in this direction was made by T. NA-KAYAMA [8], [9].M. HALL [5] treated related questions.An extensiveProof, a) According to the definition we have /.Щ1) = 0. We prove first that / n Щ1) = 0. Suppose for an indirect proof that t > = / n Щ1) Ф Ф 0. We then have 0фн/,0фк Щ1) and v> 2 с I .Щ1) = 0.The ideal
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