Abstract:The notion of a d-sequence in Commutative Algebra was introduced by Craig Huneke, while the notion of a sequence of linear type was introduced by Douglas Costa. Both types of sequences generate ideals of linear type. In this paper we study another type of sequences, that we call c-sequences. They also generate ideals of linear type. We show that c-sequences are in between d-sequences and sequences of linear type and that the initial subsequences of c-sequences are c-sequences. Finally we prove a statement which is useful for computational aspects of the theory of c-sequences.
Keywords: ideal of linear type, c-sequence, d-sequence, sequence of linear type
AMS Subject Classification: Primary 13A30, 13B25; Secondary 13A15, 13C13