# On homological classification of pomonoids by regular weak injectivity properties of S-posets

Open Mathematics (2007)

- Volume: 5, Issue: 1, page 181-200
- ISSN: 2391-5455

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topXia Zhang, and Valdis Laan. "On homological classification of pomonoids by regular weak injectivity properties of S-posets." Open Mathematics 5.1 (2007): 181-200. <http://eudml.org/doc/269136>.

@article{XiaZhang2007,

abstract = {If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.},

author = {Xia Zhang, Valdis Laan},

journal = {Open Mathematics},

keywords = {Ordered monoid; S-poset; weak injectivity; ordered monoid},

language = {eng},

number = {1},

pages = {181-200},

title = {On homological classification of pomonoids by regular weak injectivity properties of S-posets},

url = {http://eudml.org/doc/269136},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Xia Zhang

AU - Valdis Laan

TI - On homological classification of pomonoids by regular weak injectivity properties of S-posets

JO - Open Mathematics

PY - 2007

VL - 5

IS - 1

SP - 181

EP - 200

AB - If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.

LA - eng

KW - Ordered monoid; S-poset; weak injectivity; ordered monoid

UR - http://eudml.org/doc/269136

ER -

## References

top- [1] S. Bulman-Fleming and V. Laan: “Lazard’s theorem for S-posets”, Math. Nachr., Vol. 278(15), (2005), pp. 1743–1755. http://dx.doi.org/10.1002/mana.200310338 Zbl1087.06008
- [2] S. Bulman-Fleming and M. Mahmoudi: “The category of S-posets”, Semigroup Forum, Vol. 71, (2005), pp. 443–461. http://dx.doi.org/10.1007/s00233-005-0540-y Zbl1095.20047
- [3] G. Czédli and A. Lenkehegyi: “On classes of ordered algebras and quasiorder distributivity”, Acta Sci. Math. (Szeged), Vol. 46, (1983), pp. 41–54. Zbl0541.06012
- [4] V.A.R. Gould: “The characterization of monoids by properties of their S-systems”, Semigroup Forum, Vol. 32, (1985), pp. 251–265. Zbl0571.20067
- [5] V.A.R. Gould: “Coperfect monoids”, Glasg. Math. J., Vol. 29, (1987), pp. 73–88. http://dx.doi.org/10.1017/S0017089500006686 Zbl0612.20040
- [6] V.A.R. Gould: “Divisible S-systems and R-modules”, Proc. Edinburgh Math. Soc. II, Vol. 30, (1987), pp. 187–200. http://dx.doi.org/10.1017/S0013091500028261 Zbl0582.20052
- [7] M. Kilp, U. Knauer and A. Mikhalev: Monoids, Acts and Categories, Walter de Gruyter, Berlin, New York, 2000.
- [8] V. Laan: “When torsion free acts are principally weakly flat”, Semigroup Forum, Vol. 60, (2000), pp. 321–325. http://dx.doi.org/10.1007/s002339910024 Zbl0947.20051
- [9] X. Shi, Z. Liu, F. Wang and S. Bulman-Fleming: “Indecomposable, projective and flat S-posets”, Comm. Algebra, Vol. 33(1), (2005), pp. 235–251. Zbl1080.20058

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