eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Injective hulls for posemigroups; pp. 372–378

Full article in PDF format | doi: 10.3176/proc.2014.4.02

Xia Zhang, Valdis Laan


We show that injectives with respect to a specific class of order embeddings in the category of posemigroups with submultiplicative morphisms are quantales and construct injective hulls for a certain class of posemigroups with respect to this specific class of order embeddings.


  1. Adámek, J., Herrlich, H., and Strecker, G. E. Abstract and Concrete Categories: The Joy of Cats. John Wiley and Sons, New York, 1990.

  2. Bruns, G. and Lakser, H. Injective hulls of semilattices. Canad. Math. Bull., 1970, 13, 115–118.

  3. Henckell, K. and Pin, J.-E. Ordered monoids and J-trivial monoids. In Algorithmic Problems in Groups and Semigroups (Birget, J.-C., Margolis, S., Meakin, J., and Sapir, M. V., eds). Birkhäuser Boston, Boston, 2000, 121–137.

  4. Kudryavtseva, G. Ordered semigroups, upper-triangular reflexive relations and semigroups of languages. Int. J. Algebra Comput., 2010, 20, 823–832.

  5. Laan, V. and Márki, L. Strong Morita equivalence of semigroups with local units. J. Pure Appl. Algebra, 2011, 215, 2538–2546.

  6. Lambek, J., Barr, M., Kennison, J. F., and Raphael, R. Injective hulls of partially ordered monoids. Theory Appl. Categ., 2012, 26, 338–348.

  7. Maia, A. F. and Mitsch, H. Semigroups with negative natural partial order. Pure Math. Appl., 2003, 14, 289–303.

  8. Rosenthal, K. I. Quantales and Their Applications. Pitman Research Notes in Mathematics, 234, Harlow, Essex, 1990.

  9. Satyanarayana, M. Naturally totally ordered semigroups. Pacific J. Math., 1978, 77, 249–254.

10. Schein, B. M. Injectives in certain classes of semigroups. Semigroup Forum, 1974, 9, 159–171.

11. Straubing, H. and Thérien, D. Partially ordered finite monoids and a theorem of I. Simon. J. Algebra, 1988, 119, 393–399.

Back to Issue