A note on pure-semisimple rings
Xiaolei Zhang, Wei Qi
TL;DR
This paper explores various characterizations of left pure-semisimple rings through properties of pure-projective and pure-injective modules, including envelopes, covers, and limits.
Contribution
It provides new characterizations of left pure-semisimple rings based on module-theoretic properties involving pure-projective and pure-injective modules.
Findings
Characterizations via (pre)envelopes and (pre)covers
Descriptions using direct limits and sums
Insights into inverse limits and products
Abstract
In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products properties of pure-projective modules or pure-injective modules.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models