The core and dual core inverse of a morphism with factorization
Copyright policy )The core and dual core inverse of a morphism with factorization
Let [Formula: see text] be a category with an involution ∗. Suppose that [Formula: see text] is a morphism and [Formula: see text] is an (epic, monic) factorization of [Formula: see text] through [Formula: see text], then [Formula: see text] is core invertible if and only if [Formula: see text] and [Formula: see text] are both left invertible if and only if [Formula: see text], [Formula: see text] and [Formula: see text] are all essentially unique (epic, monic) factorizations of [Formula: see text] through [Formula: see text]. We also give the corresponding result about dual core inverse. In addition, we give some characterizations about the coexistence of core inverse and dual core inverse of an [Formula: see text]-morphism in the category of [Formula: see text]-modules of a given ring [Formula: see text].
- Southeast University China (People's Republic of)
Factorization systems, substructures, quotient structures, congruences, amalgams, core inverse, invertibility, Mathematics - Rings and Algebras, 15A09, 18A32, morphism, factorization, Rings and Algebras (math.RA), FOS: Mathematics, Theory of matrix inversion and generalized inverses, dual core inverse
Factorization systems, substructures, quotient structures, congruences, amalgams, core inverse, invertibility, Mathematics - Rings and Algebras, 15A09, 18A32, morphism, factorization, Rings and Algebras (math.RA), FOS: Mathematics, Theory of matrix inversion and generalized inverses, dual core inverse
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