Sequentially injective and complete acts over a semigroup

Volume 5, Issue 5, pp 345--349 http://dx.doi.org/10.22436/jnsa.005.05.04

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1817 Downloads
• 2754 Views

Authors

G. Moghaddasi - Department of Mathematics, Hakim Sabzevary University, Sabzevar, Iran.

Abstract

In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. We show that s-injectivity, s-absolutely retract, and sequential compactness are equivalent.

Share and Cite

Keywords

• sequential injective
• completeness
• absolute retract.

References

• [1] B. Banaschewsk, Injectivity and essential extensions in equational classes of algebras, Queen’s Papers in Pure and Applied Mathematics, 25 (1970), 131--147


• [2] P. Berthiaume, The injective envelope of S-Sets, Canad. Math. Bull., 10 (1967), 261--273


• [3] M. M. Ebrahimi, Algebra in a topos of sheaves: injectivity in quasi-equational classes, Pure and Appl. Alg., 26 ( 1982), 269--280


• [4] M.M. Ebrahimi, On ideal closure operators of M-sets, Southeast Asian Bulletin of mathematics, (to appear),


• [5] M.M. Ebrahimi, M. Mahmoudi, Gh. Moghaddasi Angizan, Injective hulls of acts over left zero semigroups, Semigroup Forum, 75 (2007), 212--220


• [6] M.M. Ebrahimi, M. Mahmoudi, Baer criterion and injectivity of projection algebras, Semigroup Forum, (to appear),


• [7] E. Giuli, , On m-separated projection spaces, Applied Categorical Structures, 2 (1994), 91--99


• [8] M. Kilp, U. Knauer, A. Mikhalev. Monoids, acts and categories, Walter de Gruyter, Berlin, New York (2000)