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Serial rings with krull dimension

Published online by Cambridge University Press:  18 May 2009

A. W. Chatters
A. W. Chatters
Affiliation:
School of MathematicsUniversity of BristolUniversity WalkBristol BS8 ITW
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A module is said to be serial if it has a unique chain of submodules, and a ring is serial if it is a direct sum of serial right ideals and a direct sum of serial left ideals. The serial rings of Krull dimension 0 are the Artinian serial (or generalised uniserial) rings studied by Nakayama and for which there is an extensive theory (see for example [4]). Warfield in [10] extended the theory to the non-Artinian case. In particular he showed that a Noetherian serial ring is a direct sum of Artinian serial rings and prime Noetherian serial rings, and he gave a structure theorem in the prime Noetherian case. A Noetherian non-Artinian serial ring has Krull dimension 1. Serial rings of arbitrary Krull dimension have been studied by Wright ([9], [12], [13], [14]) with special results being proved when the Krull dimension is 1 or 2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 71 - 78
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

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