Quasi-adequate semigroups. II. (English) Zbl 0747.20029
In part I [Proc. R. Soc. Edinb., Sect. A 91, 91-99 (1981; Zbl 0501.20042)] J. B. Fountain and the author introduced type \(W\) semigroups, in the present paper a weak version of this concept is considered. The main result is a generalization of P. S. Venkatesan’s structure theorem for orthodox semigroups [Semigroup Forum 20, 227-231 (1980; Zbl 0445.20036)] to such weak type \(W\) semigroups. Furthermore the largest superabundant full subsemigroup and the largest full subsemigroup (of such weak type \(W\) semigroups) which is a band of cancellative monoids is described.
Reviewer: R.F.Tichy (Graz)
MSC:
| 20M10 | General structure theory for semigroups |
Keywords:
orthodox semigroups; weak type \(W\) semigroups; superabundant full subsemigroup; band of cancellative monoidsReferences:
| [1] | El-Qallali, A.,L * -unipotent semigroups, J. Pure Appl. Algebra62 (1989), 19–33. · Zbl 0693.20060 · doi:10.1016/0022-4049(89)90018-2 |
| [2] | El-Qallali, A. and J. B. Fountain,Idempotent-connected abundant semigroups, Proc. Roy. Soc. Edinburgh A91 (1981), 79–90. · Zbl 0501.20043 |
| [3] | El-Qallali, A. and J. B. Fountain,Quasi-adequate semigroups, Proc. Roy. Soc. Edinburgh A,91 (1981), 91–99. · Zbl 0501.20042 |
| [4] | Fountain, J. B.,Adequate semigroups, Proc. Edinburgh Math. Soc.22 (1979), 113–125. · Zbl 0414.20048 · doi:10.1017/S0013091500016230 |
| [5] | Fountain, J. B.,Abundant semigroups, Proc. London Math. Soc. (3)44 (1982), 103–129. · Zbl 0481.20036 · doi:10.1112/plms/s3-44.1.103 |
| [6] | Hall, T. E.,Orthodox semigroups, Pacific J. Math.39 (1971), 677–686. · Zbl 0232.20124 |
| [7] | Howie, J. M., ”An introduction to semigroup theory”, Academic Press, London, 1976. · Zbl 0355.20056 |
| [8] | Lawson, M. V.,The natural partial order on an abundant semigroup, Proc. Edinburgh Math. Soc.30 (1987), 169–186. · Zbl 0634.20029 · doi:10.1017/S001309150002825X |
| [9] | McAlister, D. B.,One-to-one partial right translations of a right cancellation semi-group, J. Algebra43 (1976), 231–251. · Zbl 0349.20025 · doi:10.1016/0021-8693(76)90158-7 |
| [10] | Pastijn, F.,A representation of a semigroup by a semigroup of matrices over a group with zero, Semigroup Forum10 (1975), 238–249. · doi:10.1007/BF02194891 |
| [11] | Venkatesan, P. S.,Orthodox semigroups, Semigroup Forum20, (1980), 227–231. · Zbl 0445.20036 · doi:10.1007/BF02572682 |
| [12] | Venkatesan, P. S.,Certain semigroups of orthodox semigroups, Semigroup Forum32 (1985), 183–187. · Zbl 0571.20060 · doi:10.1007/BF02575535 |
| [13] | Yamada, M.,Certain subsemigroups whose idempotents form a band, Pacific. J. Math.33 (1970), n.1, 261–272. · Zbl 0199.33701 |
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