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This is a Quantitative Study study.

October 19, 2025Open Access

Some remarks on injective envelopes on ring extensions

Key Points

Every R-module has an (R,S)-injective envelope when S is a pure-semisimple ring, resolving a conjecture.
The study offers insights into the properties of (R,S)⋆-injective modules in ring extensions.
(R,S)⋆-injective modules are essential for understanding injective envelopes in this mathematical framework.
Exploring injective envelopes advances knowledge in the structure of R-modules and their extensions.

Abstract

Let f:S→R be a ring extension. We introduce and study the properties of (R,S)⋆-injective modules and the existence of (R,S)⋆-injective envelopes. Moreover, we show that every R-module has an (R,S)-injective envelope when S is a pure-semisimple ring, partly resolving a conjecture proposed by Guo Comm. Algebra 52 (2024), 2868–2883.

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Cite This Study

Xiaolei Zhang (Thu,) studied this question.

synapsesocial.com/papers/68f43efb854d1061a58ac12c https://doi.org/https://doi.org/10.4064/cm9520-5-2025

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