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Sequentially Complete S-acts and Baer Type Criteria over Semigroups

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2013

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Dedicated to Professor M. Mehdi Ebrahimi on his 65th Birthday Although the Baer Criterion for injectivity is true for modules over a ring with an identity, it is an open problem for acts over a semigroup S (with or without identity). In this work, we study a kind of Baer Criterion for injectivity of acts over a semigroup S. We consider a kind of weak injectivity which we call s -completeness and give some conditions under which s-completeness coincides with injectivity.
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  • 2
211-221
  • English

REFERENCES

References: 

[1] H. Barzegar and M.M. Ebrahimi. Sequentially pure monomorphism of acts over semigroups.
European journal of pure and applied mathematics, 1(4):41–55, 2008.
[2] H. Barzegar, M.M. Ebrahimi, and M. Mahmoudi. Essentiality and injectivity relative to
sequential purity of acts. Semigroup Forum, 79:128–144, 2009.
[3] P. Berthiaume. The injective envelope of s-sets. Canad. Math. Bull., 10(2):261–273,
1967.
[4] M.M. Ebrahimi and M. Mahmoudi. Purity and equational compactness of projection
algebras. Applied Categorical Structure, 9:381–394, 2001.
[5] M.M. Ebrahimi, M. Mahmoudi, and L. shahbaz. Proper behaviour of sequential injectivity
of acts over semigroups. Communication in Algebra, 37(7):2511–2521, 2009.
[6] E. Giuli. On m-separated projection spaces. Applied Categorical Structure, 2:91–99,
1994.
[7] V. Gould. The characterisation of monoids by properties of their s-systems. Semigroup
Forum, 32(3):251–265, 1985.
[8] V. Gould. Completely right pure monoids. Proc.Roy. Irish Acad, Section A, 87:73–82,
1987.
[9] M. Kilp, U. Knauer, and A. Mikhalev. Monoids, Acts and Categories. Walter de Gruyter,
Berlin, New York, 2000.
[10] M. Mahmoudi and Gh. Moghaddasi. Sequential purity and injectivity of acts over some
classes of semigroups. Taiwanese journal of mathematics, 15(2):733–744, 2011.
[11] M. Mahmoudi and L. Shahbaz. Characterizing semigroups by sequentially dense injective
acts. Semigroup Forum, 75(1):116–128, 2007.
[12] M. Mahmoudi and L. Shahbaz. Sequential dense essential monomorphisms of acts over
semigroups. Applied Categorical Structure, 18:461–471, 2010.

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