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

• Autorzy: Xia Zhang , Valdis Laan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Ordered monoid; S-poset; weak injectivity

Kategorie tematyczne

• 06F05: Ordered semigroups and monoids
• 20M30: Representation of semigroups; actions of semigroups on sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 1
• Strony: 181-200

Daty

wydano

2007-03-01

online

2007-03-01

Twórcy

autor

Xia Zhang

• Sun Yat-sen University

autor

Valdis Laan

• University of Tartu

Bibliografia

• [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
• [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
• [3] G. Czédli and A. Lenkehegyi: “On classes of ordered algebras and quasiorder distributivity”, Acta Sci. Math. (Szeged), Vol. 46, (1983), pp. 41–54.
• [4] V.A.R. Gould: “The characterization of monoids by properties of their S-systems”, Semigroup Forum, Vol. 32, (1985), pp. 251–265.
• [5] V.A.R. Gould: “Coperfect monoids”, Glasg. Math. J., Vol. 29, (1987), pp. 73–88. http://dx.doi.org/10.1017/S0017089500006686
• [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
• [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
• [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.

Identyfikatory

DOI

10.2478/s11533-006-0036-3