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Essentiality and injectivity relative to sequential purity of acts

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Abstract

For a class ℳ of monomorphisms of a category, mathematicians consider different types of essentiality, depending on ℳ. In this paper, considering the category of acts over a semigroup, we first briefly study the class ℳ p of a certain kind of pure monomorphisms, in a manner borrowed from V. Gould, to be called sequentially pure. Then, we study in detail three kinds of essentiality with respect to this class, and give some useful criteria to get (internal) characterizations (in terms of elements) for essentialities. Finally, the relations between injectivity, essentiality, retractness, and injective hulls, all with respect to the class of sequentially pure monomorphisms, are investigated.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, Tehran, 19839, Iran

    H. Barzegar, M. M. Ebrahimi & M. Mahmoudi

Authors
  1. H. Barzegar
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  2. M. M. Ebrahimi
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  3. M. Mahmoudi
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Corresponding author

Correspondence to M. M. Ebrahimi.

Additional information

Communicated by Steve Pride.

The second author is thankful to Iran National Science Foundation (INSF) for their financial support.

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Barzegar, H., Ebrahimi, M.M. & Mahmoudi, M. Essentiality and injectivity relative to sequential purity of acts. Semigroup Forum 79, 128–144 (2009). https://doi.org/10.1007/s00233-009-9159-8

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  • DOI: https://doi.org/10.1007/s00233-009-9159-8

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