Geodesic
Grothendieck Groups of Bass Orders
Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 103-115

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

Commutative Bass rings, which form a special class of Gorenstein rings, have been thoroughly investigated by Bass [1]. The definitions do not carry over to non-commutative rings. However, in case one deals with orders in separable algebras over fields, Bass orders can be defined. Drozd, Kiricenko, and Roïter [3] and Roïter [6] have clarified the structure of Bass orders, and they have classified them. These Bass orders play a key role in the question of the finiteness of the non-isomorphic indecomposable lattices over orders (cf. [2; 8]). We shall use the results of Drozd, Kiricenko, and Roïter [3] to compute the Grothendieck groups of Bass orders locally. Locally, the Grothendieck group of a Bass order (with the exception of one class of Bass orders) is the epimorphic image of the direct sum of the Grothendieck groups of the maximal orders containing it. 
Roggenkamp, Klaus W. Grothendieck Groups of Bass Orders. Canadian journal of mathematics, Tome 23 (1971) no. 1, pp. 103-115. doi: 10.4153/CJM-1971-011-9
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