### Citations

566 |
Fundamentals of semigroup theory
- Howie
- 1995
(Show Context)
Citation Context ... 49 As in the eventually regular case, our results give no information when the semigroup is idempotent generated. 2. Preliminaries For standard terminology and notation in semigroup theory see Howie =-=[6]-=-. The set of idempotents and regular elements in a semigroup S are denoted by E(S) and Reg(S), respectively. For any a ∈ Reg(S), we customarily denote the set of inverses of a by V (a). The lattice of... |

153 |
Lectures on Semigroups
- Petrich
- 1977
(Show Context)
Citation Context ...ences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich =-=[15]-=-, Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by means of thei... |

46 |
Structure of regular semigroups.
- Nambooripad
- 1979
(Show Context)
Citation Context ...andling congruences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich =-=[14]-=-, Petrich [15], Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by... |

12 | products of E-inversive semigroups - Mitsch - 1990 |

9 |
Eventually regular semigroups,
- Edwards
- 1983
(Show Context)
Citation Context ...ny a ∈ S (see [13]). The class of E-inversive semigroups is wide and contains many different types, for example, all regular, all eventually regular (its every element has power which is regular, see =-=[2]-=-) semigroups [12]. A semigroup is an E-semigroup if its idempotents form a subsemigroup. Congruences on regular semigroups have been explored extensively. The kernel-trace approach is an effective too... |

4 |
Certain congruences on E-inverse E-semi groups, Semi group Forum,
- Weipoltshammer
- 2002
(Show Context)
Citation Context ...group is called strongly orthodox if ρ is strongly regular. We have seen that a congruence on an eventually regular semigroup is regular if and only if it is strongly regular (see [9] or Lemma 5.4 in =-=[20]-=-). Hence a congruence on an eventually regular semigroup is orthodox if and only if it is strongly orthodox. We give a example of a strongly orthodox congruence on an E-inversive semigroup as follows.... |

3 |
Basic properties of E-inversive semigroups
- Mitsch, Petrich
(Show Context)
Citation Context ... S there exists x ∈ S such that ax is idempotent. This concept was introduced by Thierrin [17]. Hence a semigroup S is E-inversive if and only if W (a) = {a′ ∈ S : a′ = a′aa′} 6= ∅ for any a ∈ S (see =-=[13]-=-). The class of E-inversive semigroups is wide and contains many different types, for example, all regular, all eventually regular (its every element has power which is regular, see [2]) semigroups [1... |

2 |
Representation of *-congruences on regular *-semigroups
- Imaoka
- 1984
(Show Context)
Citation Context ...s an effective tool for handling congruences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka =-=[7]-=-, Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruence... |

2 |
Orthodox congruences on an eventually regular semigroup, Semigroup Forum
- Luo, Li
(Show Context)
Citation Context ...ou and Li applied this approach to eventually regular semigroups and described R-unipotent (resp., orthodox) congruences on eventually regular semigroups by means of their kernels and hyper-traces in =-=[8]-=- (resp., [9]). The purpose of this paper is to describe strongly orthodox congruences on E-inversive semigroups by means of their kernels and hyper-traces. It is shown that every strongly regular cong... |

2 |
Regular congruences on an E-inversive semigroup, Semigroup Forum
- Luo, Fan, et al.
(Show Context)
Citation Context ...the subsemigroup 〈E(S)〉 generated by E(S) and a certain normal subsemigroup K of S. These results generalize the corresponding results obtained by Lou and Li [9] for eventually regular semigroups. In =-=[11]-=- Lou et al. described strongly regular congruences on an E-inversive semigroup S by means of their kernels and traces, where the view of Pastijn and Petrich [14] was followed. Their approach gave quit... |

2 |
Kernels of Inverse Semigroups Homomorphisms
- Scheiblich
- 1974
(Show Context)
Citation Context ...semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich =-=[16]-=-, Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by means of their kernels and hyp... |

2 |
Sur les demi-groups inverses
- Thierrin
- 1952
(Show Context)
Citation Context ...long Yu 1. Introduction A semigroup S with non-empty set of idempotents is called E-inversive if for every a ∈ S there exists x ∈ S such that ax is idempotent. This concept was introduced by Thierrin =-=[17]-=-. Hence a semigroup S is E-inversive if and only if W (a) = {a′ ∈ S : a′ = a′aa′} 6= ∅ for any a ∈ S (see [13]). The class of E-inversive semigroups is wide and contains many different types, for exam... |

1 |
Congruences on *-regular semigroups
- Crvenković, Dolinka
(Show Context)
Citation Context ...red extensively. The kernel-trace approach is an effective tool for handling congruences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka =-=[1]-=-, Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then descri... |

1 |
Regular semigroup congruences
- Feigenbaum
- 1979
(Show Context)
Citation Context ... The kernel-trace approach is an effective tool for handling congruences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum =-=[3]-=-, Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent ... |

1 |
Orthodox congruences on regular semigroups
- Gomes
- 1988
(Show Context)
Citation Context ...-trace approach is an effective tool for handling congruences on regular semigroups, which had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes =-=[4]-=-, [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., ort... |

1 | The maximum idempotent-separating congruences on an eventually regular semigroup, Semigroup Forum - Luo, Li |

1 |
Normal partitions of idempotents of regular semigroups
- Trotter
- 1978
(Show Context)
Citation Context ...ich had been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter =-=[18]-=-, [19] and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by means of their kernels and hyper-traces in [... |

1 |
Congruences on regular and completely regular semigroups
- Trotter
- 1982
(Show Context)
Citation Context ...d been investigated in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], =-=[19]-=- and the author [21]. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by means of their kernels and hyper-traces in [4] (re... |

1 |
Strong P-congruences on P-regular semigroups, Semigroup Forum
- Zheng
- 1995
(Show Context)
Citation Context ...in the previous literature, such as Crvenković and Dolinka [1], Feigenbaum [3], Gomes [4], [5], Imaoka [7], Pastijn and Petrich [14], Petrich [15], Scheiblich [16], Trotter [18], [19] and the author =-=[21]-=-. Gomes developed the kernel-trace approach and then described R-unipotent (resp., orthodox) congruences on regular semigroups by means of their kernels and hyper-traces in [4] (resp., [5]). Lou and L... |