Residuated completely simple semigroups. (English) Zbl 1294.06016
Let \({S_x} = M(\left\langle x \right\rangle ;\text{I},\Lambda ;P)\) be a completely simple semigroup where \(\left\langle x \right\rangle \) is an ordered cyclic group with \(x > 1\), \({p_{11}} = {x^{ - 1}}\) and I, \(\Lambda \) are ordered, each with smallest element, \(|\text{I}|,|\Lambda | \geqslant 2\). The authors continue their investigation, started in [Commun. Algebra 29, No. 8, 3477–3494 (2001; Zbl 0993.06008)], of orders induced on \({S_x}\) by orders on I, \(\left\langle x \right\rangle\), \(\Lambda \).
Reviewer: Jaak Henno (Tallinn)
Keywords:
completely simple semigroup; induced orders; residuated; lexigrographic order; bootlace orderCitations:
Zbl 0993.06008References:
[1] | DOI: 10.1016/0021-8693(72)90112-3 · Zbl 0247.06013 · doi:10.1016/0021-8693(72)90112-3 |
[2] | DOI: 10.1080/00927879308824651 · Zbl 0776.06009 · doi:10.1080/00927879308824651 |
[3] | DOI: 10.1017/S0017089500009435 · Zbl 0725.06008 · doi:10.1017/S0017089500009435 |
[4] | DOI: 10.1017/S0013091500005770 · Zbl 0770.06006 · doi:10.1017/S0013091500005770 |
[5] | DOI: 10.1081/AGB-100105033 · Zbl 0993.06008 · doi:10.1081/AGB-100105033 |
[6] | Croisot R., Norm. Sup. 70 pp 361– (1953) |
[7] | DOI: 10.1007/BF02573443 · Zbl 0548.06007 · doi:10.1007/BF02573443 |
[8] | DOI: 10.1007/BF02572827 · Zbl 0505.06008 · doi:10.1007/BF02572827 |
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