On Some Rings Whose Modules Have Maximal Submodules

V. P. Camillo

doi:10.1090/S0002-9939-1975-0382343-9

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On Some Rings Whose Modules Have Maximal Submodules

Journal article

Open access

Peer reviewed

On Some Rings Whose Modules Have Maximal Submodules

V. P. Camillo

Proceedings of the American Mathematical Society, Vol.50(1), pp.97-100

07/01/1975

DOI: 10.1090/S0002-9939-1975-0382343-9

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Abstract

It is shown that a principal right ideal domain, having the property that every right R module has a maximal submodule must be simple. Strong conditions satisfied by these rings are deduced giving evidence for the conjecture that they must be V-rings. We also generalize an example of Faith by showing that a subring of an infinite dimensional full linear ring, which contains the socle of that ring is never a left V-ring.

Mathematics

Linear transformations

Mathematical rings

Subrings

Details

Title: Subtitle: On Some Rings Whose Modules Have Maximal Submodules
Creators: V. P. Camillo
Resource Type: Journal article
Publication Details: Proceedings of the American Mathematical Society, Vol.50(1), pp.97-100
DOI: 10.1090/S0002-9939-1975-0382343-9
ISSN: 0002-9939
eISSN: 1088-6826
Publisher: American Mathematical Society
Language: English
Date published: 07/01/1975
Academic Unit: Mathematics
Record Identifier: 9984241044002771

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