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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...

Let $K$ be a field, $A=K[X_1,\cdots ,X_n]$ and $𝕄$ the set of monomials of $A$. It is well known that the set of monomial ideals of $A$ is in a bijective correspondence with the set of all subsemiflows of the $𝕄$-semiflow $𝕄$. We generalize this to the case of term ideals of $A=R[X_1,\cdots ,X_n]$, where $R$ is a commutative Noetherian ring. A term ideal of $A$ is an ideal of $A$ generated by a family of terms $c{X}_1^{{\mu }_1}\cdots X_n^{{\mu }_n}$, where $c\in R$ and ${\mu }_1,\cdots ,{\mu }_n$ are integers $\ge 0$.