### Citations

570 |
Fundamentals of Semigroup Theory
- Howie
- 1995
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Citation Context ...f it is a semidirect product of a band and a left cancellative monoid. Factorizable Rpp Monoids 145 2 Preliminaries Throughout this paper, we adopt the terminologies and notions given in [1], [4] and =-=[7]-=-. Now we cite some known results in the literature which will be used in the sequel. To begin with, we first state some facts concerning the Green *-relations L∗ and R∗ on the semigroup S. Lemma 2.1 [... |

188 | Semigroups and Combinatorial Applications - Lallement - 1979 |

69 |
Abundant semigroups
- Fountain
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Citation Context ...ve, in short, rpp if for all a ∈ S, aS1 regarded as an S1-system is projective. We can also dually define the left principal projective semigroups (in short, lpp) semigroups. It was shown by Fountain =-=[3]-=- that a semigroup S is rpp if and only if every L∗-class of S contains at least one idempotent. According to Fountain [3] and [4], a semigroup S is called abundant if every L∗-class and every R∗-class... |

22 |
Sn-normal semigroups
- Levi, McFadden
- 1994
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Citation Context ...uence σ containing a has a greatest element ma with respect to the partial order “ ≤ ”. It is clear that F-abundant semigroups are generalized F-regular semigroups (for F-regular semigroups, see [2], =-=[10]-=- etc.) Recently, Zhang-Chen [13] considered a special subclass of F-abundant semigroups, namely, the u-IC abundant semigroups. On the other hand,Ni-Chen-Guo [11] have provided a method of construction... |

8 |
The natural partial order on an abundant semigroup
- Lawson
- 1987
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Citation Context ...uate if E(S) ,the set of idempotents of S, forms a subsemigroup of S. Regular semigroups are abundant semigroups and orthodox semigroups quasi-adequate semigroups. For an abundant semigroup S, Lawson =-=[9]-=- defined a partial order “ ≤ ” on S by a ≤ b if and only if for some e, f ∈ E(S), a = eb = bf. Later on,Guo [5] called an abundant semigroup S F-abundant if for every a ∈ S, the congruence class of th... |

5 |
F-abundant semigroups
- Guo
(Show Context)
Citation Context ...s and orthodox semigroups quasi-adequate semigroups. For an abundant semigroup S, Lawson [9] defined a partial order “ ≤ ” on S by a ≤ b if and only if for some e, f ∈ E(S), a = eb = bf. Later on,Guo =-=[5]-=- called an abundant semigroup S F-abundant if for every a ∈ S, the congruence class of the minimal cancellative congruence σ containing a has a greatest element ma with respect to the partial order “ ... |

3 |
F-regular semigroups and F-orthodox semigroups, Semigroup Forum 19(1980), 331-345. F-rpp semigroups 1585
- Edwards
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Citation Context ...congruence σ containing a has a greatest element ma with respect to the partial order “ ≤ ”. It is clear that F-abundant semigroups are generalized F-regular semigroups (for F-regular semigroups, see =-=[2]-=-, [10] etc.) Recently, Zhang-Chen [13] considered a special subclass of F-abundant semigroups, namely, the u-IC abundant semigroups. On the other hand,Ni-Chen-Guo [11] have provided a method of constr... |

2 |
Factorizable semigroups, Semigroup Forum 36
- Catino
- 1987
(Show Context)
Citation Context ...e provided a method of construction for the general F-abundant semigroups. Along this direction, Guo-Li-Shum [6] have further generalized F-abundant semigroups to F-rpp semigroups. According to Catino=-=[1]-=-,a semigroup S is called a factorizable semigroup if there exist some proper subsemigroups U and V of S such that S = UV , where UV is the set {uv | u ∈ U, v ∈ V }. In this case, we call the pair (U, ... |

2 |
F-abundant semigroups
- Ni, Chen, et al.
(Show Context)
Citation Context ...ps (for F-regular semigroups, see [2], [10] etc.) Recently, Zhang-Chen [13] considered a special subclass of F-abundant semigroups, namely, the u-IC abundant semigroups. On the other hand,Ni-Chen-Guo =-=[11]-=- have provided a method of construction for the general F-abundant semigroups. Along this direction, Guo-Li-Shum [6] have further generalized F-abundant semigroups to F-rpp semigroups. According to Ca... |

1 |
Factorizable semigroups
- Tolo
- 1969
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Citation Context ...v2]u1 = u2 and v1 = v2. We shall call a semigroup S a [left; right] univocal factorizable semigroup if no confusion arises. For researches in this topic,the readers are referred to Catino[1] and Tolo =-=[12]-=-. In this paper, we study a class of left univocal factorizable rpp semigroups, namely, the left univocal factorizable rpp monoids of type-(I,L∗). This class of left univocal factorizable rpp semigrou... |

1 |
On idempotent-connected quasi-adequate semigroups, Semigroup Forum 65
- Zhang, Chen
- 2002
(Show Context)
Citation Context ...est element ma with respect to the partial order “ ≤ ”. It is clear that F-abundant semigroups are generalized F-regular semigroups (for F-regular semigroups, see [2], [10] etc.) Recently, Zhang-Chen =-=[13]-=- considered a special subclass of F-abundant semigroups, namely, the u-IC abundant semigroups. On the other hand,Ni-Chen-Guo [11] have provided a method of construction for the general F-abundant semi... |