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Sequences between d-sequences and sequences of linear type

Hamid Kulosman — 2009

Commentationes Mathematicae Universitatis Carolinae

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...

The algebraic structure of pseudomeadow

Hamid Kulosman — 2024

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as...

A generalization of semiflows on monomials

Hamid Kulosman; Alica Miller — 2012

Mathematica Bohemica

Let $K$ be a field, $A = K [X_{1}, \dots, X_{n}]$ 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 $A = R [X_{1}, \dots, X_{n}]$ , where $R$ is a commutative Noetherian ring. A term ideal of $A$ is an ideal of $A$ generated by a family of terms $c X_{1}^{μ_{1}} \dots X_{n}^{μ_{n}}$ , where $c \in R$ and $μ_{1}, \dots, μ_{n}$ are integers $\geq 0$ .

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Currently displaying 1 – 3 of 3

Sequences between d-sequences and sequences of linear type

The algebraic structure of pseudomeadow

A generalization of semiflows on monomials