Irreducible maps of commutative rings |
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Authors: | Jeremy Haefner |
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Institution: | University of Colorado , Colorado Springs, CO, 80933 |
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Abstract: | We give necessary conditions for a map to be irreducible (in the category of finitely generated, torsion free modules) over a non-local, commutative ring and sufficient conditions when the ring is Bass. In particular, we show that an irreducible map of ZG, where G is a square free abelian group, must be a monomorphism with a simple cokernel. We also show that local endomorphism rings are necessary and sufficient for the existence of almost split sequences over a commutative Bass ring and we explicitly describe the modules and the maps in those sequences. The results in this paper enable us to describe the Auslander-Reiten quiver of a non-local Bass ring in 8]. |
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Keywords: | Primary: 16A48 Secondary: 13C05 |
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