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Hopfian and Cohopfian Objects in the Categories of Gr(A - Mod) and COMP(Gr(A - Mod))

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Listed:
  • Seydina Ababacar BALDE
  • Mohamed Ben Faraj BEN MAAOUIA
  • Ahmed Ould CHBIH

Abstract

We study in this work the notions of hopficity and cohopficity in the categories AGr(A - Mod) and COMP(AGr(A - Mod)) of associate complex to a graded left A-module and we show that- 1. Let M a graded left A-module, N a graded submodule of M, M_* be a complex associate to M. Suppose that M_* be a quasi-projective and N be a completely invariant and essential sub-complex of M_* associate to N. Then N_* is cohopfian if, and only, if M_* is cohopfian. 2. Let M a graded left A-module, N a graded submodule of M, M_* quasi-injective and M_* a completely invariant and superfluous sub-complex of M_*. Then M_* is cohopfian if, and only, if M_*=M_* is cohopfian.

Suggested Citation

  • Seydina Ababacar BALDE & Mohamed Ben Faraj BEN MAAOUIA & Ahmed Ould CHBIH, 2020. "Hopfian and Cohopfian Objects in the Categories of Gr(A - Mod) and COMP(Gr(A - Mod))," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(2), pages 1-17, April.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:2:p:17
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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