Hopfian and Cohopfian Objects in the Categories of Gr(A - Mod) and COMP(Gr(A - Mod))
Seydina Ababacar Balde,
Mohamed Ben Faraj BEN Maaouia and
Ahmed Ould Chbih
Journal of Mathematics Research, 2020, vol. 12, issue 2, 17
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.
JEL-codes: R00 Z0 (search for similar items in EconPapers)
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