• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1215-1231
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• 2023

In this paper, we investigate the nonnil-exact sequences and nonnil-commutative diagrams and show that they behave in a way similar to the classical ones in Abelian categories.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.1-14
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• 2024

Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative diagrams and nonnil-projective modules. They proved that an R-module that is nonnil-isomorphic to a projective module is nonnil-projective, and they proposed the following problem: Is every nonnil-projective module nonnil-isomorphic to some projective module? In this paper, we delve into some new properties of nonnil-commutative diagrams and answer this problem in the affirmative.