Certain partial orders on semigroups

Mario Petrich

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 415-432
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Petrich, Mario. "Certain partial orders on semigroups." Czechoslovak Mathematical Journal 51.2 (2001): 415-432. <http://eudml.org/doc/30644>.

@article{Petrich2001,
abstract = {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.},
author = {Petrich, Mario},
journal = {Czechoslovak Mathematical Journal},
keywords = {semigroup; regular; completely semisimple; completely regular; band of groups; normal band of groups; partial order; compatible with multiplication; coincidence of relations; completely semisimple semigroups; completely regular semigroups; normal bands of groups; partial orders; compatibility with multiplication; coincidence of relations},
language = {eng},
number = {2},
pages = {415-432},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Certain partial orders on semigroups},
url = {http://eudml.org/doc/30644},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Petrich, Mario
TI - Certain partial orders on semigroups
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 415
EP - 432
AB - 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.
LA - eng
KW - semigroup; regular; completely semisimple; completely regular; band of groups; normal band of groups; partial order; compatible with multiplication; coincidence of relations; completely semisimple semigroups; completely regular semigroups; normal bands of groups; partial orders; compatibility with multiplication; coincidence of relations
UR - http://eudml.org/doc/30644
ER -

References

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  9. 10.1090/S0002-9947-1972-0304522-0, Trans. Amer. Math. Soc. 170 (1972), 245–269. (1972) Zbl0257.20056MR0304522DOI10.1090/S0002-9947-1972-0304522-0
  10. Introduction to Semigroups, Merrill. Columbus, Ohio, 1973, pp. . (1973) Zbl0321.20037MR0393206
  11. Inverse Semigroups, Wiley, New York, 1984, pp. . (1984) Zbl0546.20053MR0752899
  12. 10.1007/BF02676644, Semigroup Forum 23 (1981), 201–220. (1981) MR0647112DOI10.1007/BF02676644
  13. 10.1007/BF01360238, Math. Ann. 136 (1958), 326–338. (1958) Zbl0083.02902MR0100563DOI10.1007/BF01360238

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