Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
semigroup; completely regular; variety; lattice; relation; kernel; trace; local relation; core
semigroup; completely regular; variety; lattice; relation; kernel; trace; local relation; core
Summary:
Completely regular semigroups $\mathcal {CR}$ are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes $\mathcal {CR}$ a variety; its lattice of subvarieties is denoted by $\mathcal {L(CR)}$. We study here the relations ${\mathbf K,T,L}$ and ${\mathbf C}$ relative to a sublattice $\Psi $ of $\mathcal {L(CR)}$ constructed in a previous publication. \endgraf For ${\mathbf R}$ being any of these relations, we determine the ${\mathbf R}$-classes of all varieties in the lattice $\Psi $ as well as the restrictions of ${\mathbf R}$ to $\Psi $.
References:
[1] Kad'ourek, J.: On the word problem for free bands of groups and for free objects in some other varieties of completely regular semigroups. Semigroup Forum 38 (1989), 1-55. DOI 10.1007/BF02573217 | MR 0961825 | Zbl 0661.20037
[2] Pastijn, F.: The lattice of completely regular semigroup varieties. J. Aust. Math. Soc., Ser. A 49 (1990), 24-42. DOI 10.1017/s1446788700030214 | MR 1054080 | Zbl 0706.20042
[3] Petrich, M.: Some relations on the lattice of varieties of completely regular semigroups. Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat., VIII. Ser. 5 (2002), 265-278. MR 1911191 | Zbl 1072.20067
[4] Petrich, M.: Canonical varieties of completely regular semigroups. J. Aust. Math. Soc. 83 (2007), 87-104. DOI 10.1017/S1446788700036405 | MR 2378436 | Zbl 1142.20035
[5] Petrich, M.: A lattice of varieties of completely regular semigroups. Commun. Algebra 42 (2014), 1397-1413. DOI 10.1080/00927872.2012.667181 | MR 3169638 | Zbl 1302.20059
[6] Petrich, M.: Certain relations on a lattice of varieties of completely regular semigroups. Commun. Algebra 43 (2015), 4080-4096. DOI 10.1080/00927872.2014.907412 | MR 3366561 | Zbl 1339.20053
[7] Petrich, M.: Varieties of completely regular semigroups related to canonical varieties. Semigroup Forum 90 (2015), 53-99. DOI 10.1007/s00233-014-9591-2 | MR 3297810 | Zbl 1328.20077
[8] Petrich, M.: Some relations on a semilattice of varieties of completely regular semigroups. Semigroup Forum 93 (2016), 607-628. DOI 10.1007/s00233-016-9817-6 | MR 3572420 | Zbl 06688592
[9] Petrich, M.: Another lattice of varieties of completely regular semigroups. Commun. Algebra 45 (2017), 2783-2794. DOI 10.1080/00927872.2016.1233190 | MR 3594557 | Zbl 1373.20072
[10] Petrich, M., Reilly, N. R.: Semigroups generated by certain operators on varieties of completely regular semigroups. Pac. J. Math. 132 (1988), 151-175. DOI 10.2140/pjm.1988.132.151 | MR 0929587 | Zbl 0598.20061
[11] Petrich, M., Reilly, N. R.: Operators related to $E$-disjunctive and fundamental completely regular semigroups. J. Algebra 134 (1990), 1-27. DOI 10.1016/0021-8693(90)90207-5 | MR 1068411 | Zbl 0706.20043
[12] Petrich, M., Reilly, N. R.: Operators related to idempotent generated and monoid completely regular semigroups. J. Aust. Math. Soc., Ser. A 49 (1990), 1-23. DOI 10.1017/s1446788700030202 | MR 1054079 | Zbl 0708.20019
[13] Petrich, M., Reilly, N. R.: Completely Regular Semigroups. Canadian Mathematical Society Series of Monographs and Advanced Texts 23. A Wiley-Interscience Publication. John Wiley & Sons, Chichester (1999). MR 1684919 | Zbl 0967.20034
[14] Polák, L.: On varieties of completely regular semigroups. I. Semigroup Forum 32 (1985), 97-123. DOI 10.1007/BF02575527 | MR 0803483 | Zbl 0564.20034
[15] Polák, L.: On varieties of completely regular semigroups. II. Semigroup Forum 36 (1988), 253-284. DOI 10.1007/BF02575021 | MR 0916425 | Zbl 0638.20032
[16] Reilly, N. R., Zhang, S.: Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands. Algebra Univers. 44 (2000), 217-239. DOI 10.1007/s000120050183 | MR 1816020 | Zbl 1013.08010
Search
Partner of
