In this article we explicitly give a description to compute the type sequence t_1, . . . , t_n of a semigroup S generated by an arithmetic sequence explicitly ; we show that the i-th term t_i is equal to 1 or to the type , depending on its position. Further, for analytically irreducible ring R with the branch sequence R_j ,we give a characterization of the “Arf” property using the type sequence of R and of the rings R_j . Further, we prove some relations among the integers l*(R) and l*(R_j ) . These relations allow us to obtaina new charaterization of semigroup rings of minimal multiplicity with l*(R)≤ type (R) in terms of the Arf property, type sequences and relations between l*(R) and l*(Rj ) .
On type sequences and Arf rings
TAMONE, GRAZIA
2007-01-01
Abstract
In this article we explicitly give a description to compute the type sequence t_1, . . . , t_n of a semigroup S generated by an arithmetic sequence explicitly ; we show that the i-th term t_i is equal to 1 or to the type , depending on its position. Further, for analytically irreducible ring R with the branch sequence R_j ,we give a characterization of the “Arf” property using the type sequence of R and of the rings R_j . Further, we prove some relations among the integers l*(R) and l*(R_j ) . These relations allow us to obtaina new charaterization of semigroup rings of minimal multiplicity with l*(R)≤ type (R) in terms of the Arf property, type sequences and relations between l*(R) and l*(Rj ) .
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