In [6] was proved that if R is a principal ideal domain and N ⊂ M are submodules of R[x1, . . . , xn], then the primary decomposition for N in M can be computed using Gröbner bases. In this paper we extend this result to Dedekind domains. The procedure that computed the primary decomposition is illustrated with an example.

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hype...

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

pediatric traumatic limb amputations are rare and their acute and long term management can be challenging in this subgroup of patients. the lengthy and costly hospital stays, and resulting physical and psychological implications leads to significant morbidity. we present a summary of treatment principles and the evidence base supporting the management options for this entity. the initial manage...

A Survey of Primary Decomposition using GrSbner Bases MICHELLE WILSON Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Science We present a survey of primary decomposition of ideals in a noetherian commutative polynomial ring R[x] = R[xi,..., x,]. With the use of ideal operations introduced and the lexicographical Gr6bner bases of...

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...