eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2021): 1.024
Morita theorems for partially ordered monoids; pp. 221–237
PDF | doi: 10.3176/proc.2011.4.03

Valdis Laan

Two partially ordered monoids S and T are called Morita equivalent if the categories of right S-posets and right T-posets are Pos-equivalent as categories enriched over the category Pos of posets. We give a description of Pos-prodense biposets and prove Morita theorems I, II, and III for partially ordered monoids.


  1. Anderson, F. and Fuller, K. Rings and Categories of Modules. Springer-Verlag, Berlin, New York, 1974.

  2. Banaschewski, B. Functors into categories of M-sets. Abh. Math. Sem. Univ. Hamburg, 1972, 38, 49–64.

  3. Bulman-Fleming, S. and Mahmoudi, M. The category of S-posets. Semigroup Forum, 2005, 71, 443–461.

  4. Kilp, M., Knauer, U., and Mikhalev, A. Monoids, Acts and Categories. Walter de Gruyter, Berlin, New York, 2000.

  5. Knauer, U. Projectivity of acts and Morita equivalence of monoids. Semigroup Forum, 1972, 3, 359–370.

  6. Laan, V. Generators in the category of S-posets. Cent. Eur. J. Math., 2008, 6, 357–363.

  7. Lam, T. Y. Lectures on Modules and Rings. Springer-Verlag, New York, 1999.

  8. Lawson, M. V. Enlargements of regular semigroups. Proc. Edinburgh Math. Soc., 1996, 39, 425–460.

  9. Lawson, M. V. Morita equivalence of semigroups with local units. J. Pure Appl. Algebra, 2011, 215, 455–470.

10. Lindner, H. Morita equivalences of enriched categories. Cah. Topol. Géom. Différ., 1974, 15, 377–397.

11. Shi, X. Strongly flat and po-flat S-posets. Comm. Algebra, 2005, 33, 4515–4531.

12. Shi, X., Liu, Z., Wang, F., and Bulman-Fleming, S. Indecomposable, projective and flat S-posets. Comm. Algebra, 2005, 33, 235–251.

Back to Issue