Geodesic
On the Irreducible Lattices of Orders
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 970-976

Voir la notice de l'article provenant de la source Cambridge University Press

We shall use the following notation: R = Dedekind domain; K = quotient field of R; Rp = ring of p-adic integers in K, p being a prime ideal in R; A = finite-dimensional separable k-algebra; G – R-order in A (for the definition cf. (3)).All modules that occur are assumed to be finitely generated unitary left modules, unless otherwise specified. By a G-lattice we mean a G-module which is torsion-free as R-module. A G-lattice is called irreducible if it does not contain a proper G-submodule of smaller R-rank. If p is a prime ideal in R we shall write Gp = Rp ⊗RG; Mp = RP⊗RM for a G-lattice M, and KM = K ⊗R M. Two G-lattices M and N are said to lie in the same genus (notation M ∨ N) if Mp ≌ Np for every prime ideal p in R.For any A-module L, let S(L) be the collection of G-lattices M, for which KM ≌ L. Suppose that S(L) splits into rg(L) genera, and into ri(L) classes under G-isomorphism. Maranda (6) has shown: If L is an absolutely irreducible A-module, then 
Roggenkamp, Klaus W. On the Irreducible Lattices of Orders. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 970-976. doi: 10.4153/CJM-1969-106-x
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