The $\\lambda$-dimension of commutative arithmetic rings

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

It is shown that every commutative arithmetic ring $R$ has $lambda$-dimension $\\leq 3$. An example of a commutative Kaplansky ring with $\\lambda$-dimension 3 is given. If $R$ satisfies an additional condition then $\\lambda$-dim($R$)<3.

Mots clés: arithmetic ring; $\\lambda$-dimension; Kaplansky ring; Bezout ring; valuation ring

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. The $\\lambda$-dimension of commutative arithmetic rings. Communications in Algebra, 2003, 31, pp.3143-3158. ⟨10.1081/AGB-120022216⟩. ⟨hal-00002948⟩