Exact embedding functors and left coherent rings

Authors:
Kent R. Fuller and George Hutchinson

Journal:
Proc. Amer. Math. Soc. **104** (1988), 385-391

MSC:
Primary 16A89; Secondary 18E20

DOI:
https://doi.org/10.1090/S0002-9939-1988-0962803-9

MathSciNet review:
962803

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Abstract: Let and be rings with unit. Suppose is a free -module on generators, where is an infinite cardinal number not smaller than the cardinality of , and is the ring of endomorphisms .

Theorem. *If* *is left coherent and there exists an exact embedding functor* , *then* *is a bimodule such that* *is faithfully flat*.

Theorem. *If* *is an exact embedding functor, then* *is a bimodule such that* *is a projective generator (inducing an exact embedding* Hom *functor from* *into* ,) *and* *is a bimodule such that* *is faithfully flat (inducing an exact embedding tensor product functor* -- *from* *into* .)

Theorem. *There exists an exact embedding functor* *iff there exists an* *-module* *and a unit-preserving ring monomorphism* *of their endomorphism rings, such that* *preserves and reflects exact pairs of endomorphisms*.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0962803-9

Article copyright:
© Copyright 1988
American Mathematical Society