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Torsion theoretic points and spaces

Published online by Cambridge University Press:  14 November 2011

Harold Simmons
Harold Simmons
Affiliation:
Department of Mathematics, University of Aberdeen, Aberdeen AB9 2TY
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Synopsis

For each ring R, we construct a topological space pt (R) which includes as a subspace both the classical spectrum specR and the torsion theoretic spectrum R-sp. For many rings (e.g. rings with Krull dimension), spec R is a retract of pt (R) and the retraction map θ generalizes the Gabriel correspondence for noetherian rings. There is a natural decomposition theory on MOD-R which extends the Goldman theory in the same way that the tertiary theory extends the primary theory. The map θ provides a direct comparison between this new decomposition theory and the tertiary theory. The space pt (R) is closely connected with the lattice of hereditary torsion theories on R, and for fully bounded (not necessarily noetherian) R, this connection is very tight.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 345 - 361
Copyright
Copyright © Royal Society of Edinburgh 1984

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