The Arithmetic of the Quasi-Uniserial Semigroups without Zero
1971; Cambridge University Press; Volume: 23; Issue: 3 Linguagem: Inglês
10.4153/cjm-1971-054-6
ISSN1496-4279
Autores Tópico(s)Rings, Modules, and Algebras
ResumoAn element a in a partially ordered semigroup T is called integral if is valid. The integral elements form a subsemigroup S of T if they exist. Two different integral idempotents e and f in T generate different one-sided ideals, because eT = fT , say, implies e = fe ⊆ f and f = ef ⊆ e . Let M be a completely simple semigroup. M is the disjoint union of its maximal subgroups [ 4 ]. Their identity elements generate the minimal one-sided ideals in M . The previous paragraph suggests the introduction of the following hypothesis on M . Hypothesis 1. Every minimal one-sided ideal in M is generated by an integral idempotent.
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