Lattices of normally indecomposable modules
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- by Juliusz Brzezinski PDF
- Proc. Amer. Math. Soc. 68 (1978), 271-276 Request permission
Abstract:
If M, N are finitely generated left R-modules, then M divides ${N^1}$ if there is an epimorphism ${M^{(r)}} \to N$. M is normally indecomposable if $M \cong {M_1} \oplus {M_2}$ and ${M_1}$ divides ${M_2}$ imply ${M_2} = 0$. If R is an Artin algebra or an order over a complete discrete valuation ring in a semisimple algebra, the set of isomorphism classes of normally indecomposable R-modules (respectively R-lattices) is partially ordered by the divisibility relation. We show that for R of finite representation type this partially ordered set is a lattice satisfying the Jordan-Dedekind chain condition and the length of maximal chains is equal to the number of isomorphism classes of indecomposable R-modules (respectively R-lattices).References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 271-276
- MSC: Primary 16A64; Secondary 16A46, 18E05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0469979-4
- MathSciNet review: 0469979