| Title:
|
Certain partial orders on semigroups (English) |
| Author:
|
Petrich, Mario |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
415-432 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
regular |
| Keyword:
|
completely semisimple |
| Keyword:
|
completely regular |
| Keyword:
|
band of groups |
| Keyword:
|
normal band of groups |
| Keyword:
|
partial order |
| Keyword:
|
compatible with multiplication |
| Keyword:
|
coincidence of relations |
| MSC:
|
06A06 |
| MSC:
|
06F05 |
| MSC:
|
20M10 |
| MSC:
|
20M17 |
| idZBL:
|
Zbl 0983.20056 |
| idMR:
|
MR1844320 |
| . |
| Date available:
|
2009-09-24T10:43:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127657 |
| . |
| Reference:
|
[1] W. D. Burgess and R. Raphael: On Conrad’s partial order relation on semiprime rings and on semigroups.Semigroup Forum 16 (1978), 133–140. MR 0491395, 10.1007/BF02194622 |
| Reference:
|
[2] A. H. Clifford and G. B. Preston: The algebraic theory of semigroups, Vol I.Math. Surveys No. 7, Amer. Math. Soc., Providence, 1961. MR 0132791 |
| Reference:
|
[3] P. F. Conrad: The hulls of semiprime rings.Bull. Austral. Math. Soc. 12 (1975), 311–314. Zbl 0297.16003, MR 0374177, 10.1017/S0004972700023911 |
| Reference:
|
[4] M. P. Drazin: A partial order in completely regular semigroups.J. Algebra 98 (1986), 362–374. Zbl 0578.20057, MR 0826133, 10.1016/0021-8693(86)90003-7 |
| Reference:
|
[5] R. E. Hartwig: How to partially order regular elements.Math. Japon. 25 (1980), 1–13. Zbl 0442.06006, MR 0571255 |
| Reference:
|
[6] E. Hewitt and H. S. Zuckerman: The $l_1$-algebra of a commutative semigroup.Trans. Amer. Math. Soc. 83 (1956), 70–97. MR 0081908 |
| Reference:
|
[7] H. Mitsch: A natural partial order for semigroups.Proc. Amer. Math. Soc. 97 (1986), 384–388. Zbl 0596.06015, MR 0840614, 10.1090/S0002-9939-1986-0840614-0 |
| Reference:
|
[8] K. S. S. Nambooripad: The natural partial order on a regular semigroup.Proc. Edinburgh Math. Soc. 23 (1980), 249–260. Zbl 0459.20054, MR 0620922 |
| Reference:
|
[9] M. Petrich: Regular semigroups satisfying certain conditions on idempotents and ideals.Trans. Amer. Math. Soc. 170 (1972), 245–269. Zbl 0257.20056, MR 0304522, 10.1090/S0002-9947-1972-0304522-0 |
| Reference:
|
[10] M. Petrich: Introduction to Semigroups.Merrill. Columbus, Ohio, 1973, pp. . Zbl 0321.20037, MR 0393206 |
| Reference:
|
[11] M. Petrich: Inverse Semigroups.Wiley, New York, 1984, pp. . Zbl 0546.20053, MR 0752899 |
| Reference:
|
[12] V. V. Rasin: On the variety of Cliffordean semigroups.Semigroup Forum 23 (1981), 201–220. MR 0647112, 10.1007/BF02676644 |
| Reference:
|
[13] I. Sussman: A generalization of Boolean rings.Math. Ann. 136 (1958), 326–338. Zbl 0083.02902, MR 0100563, 10.1007/BF01360238 |
| . |
