Let R be a Dedekind domain with quotient field K and let R be the integral closure of R in an algebraic closure of K. Let r be the set of rings A such that A is finitely generated over R and R C A C R. Let r(~be) th e set of rings 0 such that 0 is finitely generated over R(g) and R(g) C 0 C R(IL). We introduce an equivalence relation on r(g) and prove that the properties of a ring A E r can be explicitly derived from the properties of an element equivalent to A(%) and monogenic. This allows to generalize Dedekind's criterion, to describe prime ideals, the P-radical and primary decomposition in A as well as to generalize Kummer's factorization theorem to all Dedekind domains
Kronecker's method of indeterminate coefficients
DEL CORSO, ILARIA
2000-01-01
Abstract
Let R be a Dedekind domain with quotient field K and let R be the integral closure of R in an algebraic closure of K. Let r be the set of rings A such that A is finitely generated over R and R C A C R. Let r(~be) th e set of rings 0 such that 0 is finitely generated over R(g) and R(g) C 0 C R(IL). We introduce an equivalence relation on r(g) and prove that the properties of a ring A E r can be explicitly derived from the properties of an element equivalent to A(%) and monogenic. This allows to generalize Dedekind's criterion, to describe prime ideals, the P-radical and primary decomposition in A as well as to generalize Kummer's factorization theorem to all Dedekind domainsI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
