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Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if… Click to show full abstract
Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator [Formula: see text] is a finitely generated left ideal of Mn(S) for any M-m-generated submodule X of Mn if and only if every M-(n, m)-presented right R-module has an add M-preenvelope. As a consequence, we investigate when the endomorphism ring S is left coherent, left pseudo-coherent, left semihereditary or von Neumann regular.
Keywords:
coherent;
whose endomorphism;
endomorphism rings;
modules whose;
endomorphism;
rings coherent
Journal Title: Algebra Colloquium
Year Published: 2019
Link to full text (if available)
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Journal Title: Algebra Colloquium
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!