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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