Abstract
ABSTRACT Let ℒ be a class of right R-modules. The notions of ℒ-injectivity and ℒ-flatness are used to investigate right ℒ-Noetherian rings, right ℒ-hereditary rings, and right ℒ-coherent rings. For an almost excellent extension S ≥ R, if either ring is the above-mentioned ring, so is the other. Specializing the class ℒ, some known results can be obtained and extended as corollaries.
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