Geodesic
The Arithmetic of the Quasi-Uniserial Semigroups without Zero
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 507-516

Voir la notice de l'article provenant de la source Cambridge University Press

An 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. 
Behrens, Ernst August. The Arithmetic of the Quasi-Uniserial Semigroups without Zero. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 507-516. doi: 10.4153/CJM-1971-054-6
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[1] 1. Behrens, E. A., Partially ordered completely simple semigroups, to appear in J. Algebra. Preprint: Math. Report McMaster University No. 22, vol. 2 (1970). Google Scholar

[2] 2. Behrens, E. A., D*-arithmetic prime rings, Math. Report McMaster University No. 24, vol. 2 (1970). Google Scholar

[3] 3. Behrens, E. A., The quasi-uniserial semigroups without zero, their arithmetics and their ϕ*-algebras, Semigroup Forum, to appear. Google Scholar

[4] 4. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups (Vol. 1, Mathematical Surveys, No. 7, American-Mathematical Society, Providence, 1961). Google Scholar

[5] 5. Rees, D., On semigroups, Proc. Cambridge Philos. Soc. 36 (1940), 387–400. Google Scholar

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