| Title:
|
Relations on a lattice of varieties of completely regular semigroups (English) |
| Author:
|
Petrich, Mario |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
225-240 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 $. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
completely regular |
| Keyword:
|
variety |
| Keyword:
|
lattice |
| Keyword:
|
relation |
| Keyword:
|
kernel |
| Keyword:
|
trace |
| Keyword:
|
local relation |
| Keyword:
|
core |
| MSC:
|
20M07 |
| idZBL:
|
07250707 |
| idMR:
|
MR4221831 |
| DOI:
|
10.21136/MB.2019.0050-18 |
| . |
| Date available:
|
2020-09-14T14:59:21Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148345 |
| . |
| Reference:
|
[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. Zbl 0661.20037, MR 0961825, 10.1007/BF02573217 |
| Reference:
|
[2] Pastijn, F.: The lattice of completely regular semigroup varieties.J. Aust. Math. Soc., Ser. A 49 (1990), 24-42. Zbl 0706.20042, MR 1054080, 10.1017/s1446788700030214 |
| Reference:
|
[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. Zbl 1072.20067, MR 1911191 |
| Reference:
|
[4] Petrich, M.: Canonical varieties of completely regular semigroups.J. Aust. Math. Soc. 83 (2007), 87-104. Zbl 1142.20035, MR 2378436, 10.1017/S1446788700036405 |
| Reference:
|
[5] Petrich, M.: A lattice of varieties of completely regular semigroups.Commun. Algebra 42 (2014), 1397-1413. Zbl 1302.20059, MR 3169638, 10.1080/00927872.2012.667181 |
| Reference:
|
[6] Petrich, M.: Certain relations on a lattice of varieties of completely regular semigroups.Commun. Algebra 43 (2015), 4080-4096. Zbl 1339.20053, MR 3366561, 10.1080/00927872.2014.907412 |
| Reference:
|
[7] Petrich, M.: Varieties of completely regular semigroups related to canonical varieties.Semigroup Forum 90 (2015), 53-99. Zbl 1328.20077, MR 3297810, 10.1007/s00233-014-9591-2 |
| Reference:
|
[8] Petrich, M.: Some relations on a semilattice of varieties of completely regular semigroups.Semigroup Forum 93 (2016), 607-628. Zbl 06688592, MR 3572420, 10.1007/s00233-016-9817-6 |
| Reference:
|
[9] Petrich, M.: Another lattice of varieties of completely regular semigroups.Commun. Algebra 45 (2017), 2783-2794. Zbl 1373.20072, MR 3594557, 10.1080/00927872.2016.1233190 |
| Reference:
|
[10] Petrich, M., Reilly, N. R.: Semigroups generated by certain operators on varieties of completely regular semigroups.Pac. J. Math. 132 (1988), 151-175. Zbl 0598.20061, MR 0929587, 10.2140/pjm.1988.132.151 |
| Reference:
|
[11] Petrich, M., Reilly, N. R.: Operators related to $E$-disjunctive and fundamental completely regular semigroups.J. Algebra 134 (1990), 1-27. Zbl 0706.20043, MR 1068411, 10.1016/0021-8693(90)90207-5 |
| Reference:
|
[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. Zbl 0708.20019, MR 1054079, 10.1017/s1446788700030202 |
| Reference:
|
[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). Zbl 0967.20034, MR 1684919 |
| Reference:
|
[14] Polák, L.: On varieties of completely regular semigroups. I.Semigroup Forum 32 (1985), 97-123. Zbl 0564.20034, MR 0803483, 10.1007/BF02575527 |
| Reference:
|
[15] Polák, L.: On varieties of completely regular semigroups. II.Semigroup Forum 36 (1988), 253-284. Zbl 0638.20032, MR 0916425, 10.1007/BF02575021 |
| Reference:
|
[16] Reilly, N. R., Zhang, S.: Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands.Algebra Univers. 44 (2000), 217-239. Zbl 1013.08010, MR 1816020, 10.1007/s000120050183 |
| . |
