# Conditions for strong Morita equivalence of partially ordered semigroups

Open Mathematics (2011)

- Volume: 9, Issue: 5, page 1100-1113
- ISSN: 2391-5455

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topLauri Tart. "Conditions for strong Morita equivalence of partially ordered semigroups." Open Mathematics 9.5 (2011): 1100-1113. <http://eudml.org/doc/269423>.

@article{LauriTart2011,

abstract = {We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.},

author = {Lauri Tart},

journal = {Open Mathematics},

keywords = {Ordered semigroup; Strong Morita equivalence; Morita invariant; ordered semigroup; strong Morita equivalence; local unit; weak local unit},

language = {eng},

number = {5},

pages = {1100-1113},

title = {Conditions for strong Morita equivalence of partially ordered semigroups},

url = {http://eudml.org/doc/269423},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Lauri Tart

TI - Conditions for strong Morita equivalence of partially ordered semigroups

JO - Open Mathematics

PY - 2011

VL - 9

IS - 5

SP - 1100

EP - 1113

AB - We investigate when a partially ordered semigroup (with various types of local units) is strongly Morita equivalent to a posemigroup from a given class of partially ordered semigroups. Necessary and sufficient conditions for such equivalence are obtained for a series of well-known classes of posemigroups. A number of sufficient conditions for several classes of naturally ordered posemigroups are also provided.

LA - eng

KW - Ordered semigroup; Strong Morita equivalence; Morita invariant; ordered semigroup; strong Morita equivalence; local unit; weak local unit

UR - http://eudml.org/doc/269423

ER -

## References

top- [1] Banaschewski B., Functors into categories of M-sets, Abh. Math. Semin. Univ. Hamburg, 1972, 38, 49–64 http://dx.doi.org/10.1007/BF02996922 Zbl0257.18011
- [2] Bass H., The Morita Theorems, lecture notes, University of Oregon, Eugene, Oregon, 1962
- [3] Bulman-Fleming S., Flatness properties of S-posets: an overview, In: Proceedings of the International Conference on Semigroups, Acts and Categories with Applications to Graphs, Tartu, June 27–30, 2007, Math. Stud. (Tartu), 3, Estonian Mathematical Society, Tartu, 2008, 28–40 Zbl1173.20042
- [4] Laan V., Context equivalence of semigroups, Period. Math. Hungar., 2010, 60(1), 81–94 http://dx.doi.org/10.1007/s10998-010-1081-z Zbl1214.20061
- [5] Laan V., Márki L., Strong Morita equivalence of semigroups with local units, J. Pure Appl. Algebra, 2011, 215(10), 2538–2546 http://dx.doi.org/10.1016/j.jpaa.2011.02.017 Zbl1237.20057
- [6] Laan V., Márki L., Morita invariants for semigroups with local units, Monatsh. Math (in press), DOI: 10.1007/s00605-010-0279-8 Zbl1256.20054
- [7] Lawson M.V., Morita equivalence of semigroups with local units, J. Pure Appl. Algebra, 2011, 215(4), 455–470 http://dx.doi.org/10.1016/j.jpaa.2010.04.030 Zbl1229.20060
- [8] McAlister D.B., Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups, J. Austral. Math. Soc. Ser. A, 1981, 31(3), 325–336 http://dx.doi.org/10.1017/S1446788700019467 Zbl0474.06015
- [9] McAlister D.B., Rees matrix covers for locally inverse semigroups, Trans. Amer. Math. Soc., 1983, 277(2), 727–738 http://dx.doi.org/10.1090/S0002-9947-1983-0694385-3 Zbl0516.20039
- [10] McAlister D.B., Rees matrix covers for regular semigroups, J. Algebra, 1984, 89(2), 264–279 http://dx.doi.org/10.1016/0021-8693(84)90217-5 Zbl0543.20041
- [11] McAlister D.B., Blyth T.S., Split orthodox semigroups, J. Algebra, 1978, 51(2), 491–525 http://dx.doi.org/10.1016/0021-8693(78)90118-7 Zbl0391.20043
- [12] Nambooripad K.S.S., The natural partial order on a regular semigroup, Proc. Edinb. Math. Soc., 1980, 23(3), 249–260 http://dx.doi.org/10.1017/S0013091500003801 Zbl0459.20054
- [13] Neklyudova V.V., Polygons under semigroups with a system of local units, Fundam. Prikl. Mat., 1997, 3(3), 879–902 (in Russian) Zbl0932.20056
- [14] Neklyudova V.V., Morita equivalence of semigroups with a system of local units, Fundam. Prikl. Mat., 1999, 5(2), 539–555 (in Russian) Zbl0963.20035
- [15] Talwar S., Morita equivalence for semigroups, J. Austral. Math. Soc. Ser. A, 1995, 59(1), 81–111 http://dx.doi.org/10.1017/S1446788700038489
- [16] Talwar S., Strong Morita equivalence and a generalisation of the Rees theorem, J. Algebra, 1996, 181(2), 371–394 http://dx.doi.org/10.1006/jabr.1996.0125 Zbl0855.20054
- [17] Tart L., Morita equivalence for ordered semigroups with local units, Period. Math. Hungar. (in press) Zbl1289.06024
- [18] Tart L., On Morita equivalence of partially ordered semigroups with local units, Acta Comment. Univ. Tartu. Math. (in press)
- [19] Tart L., Characterizations of strong Morita equivalence for ordered semigroups with local units (submitted)

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