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On von Neumann regular rings. X. (English) Zbl 0544.16006

[Part IX, cf. the article reviewed above.]
In the first part of the paper, rings having a regular classical left quotient ring Q are considered and conditions for Q to be continuous, reduced, strongly regular and semi-simple Artinian are studied. In the second part, the following definition is introduced: A left A-module M is called an NCI module if, for any left submodule P containing a non-zero complement left submodule of M and any left submodule N of M which is isomorphic to P, every left A-homomorphism of N into P extends to an endomorphism of M. Injective modules are NCI and NCI-modules are continuous. The author connects this definition with various other notions, such as regular, strongly regular, quasi-Frobenius and semi- simple Artinian rings (e.g. A is semi-simple Artinian iff every finitely generated left module is NCI).
Reviewer: H.H.Storrer

MSC:

16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D50 Injective modules, self-injective associative rings
16Kxx Division rings and semisimple Artin rings

Citations:

Zbl 0544.16005
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