In recent years, the combinatorial properties of monomials ideals [7, 10, 14] and binomial ideals [9, 10] have been widely studied. In particular, combinatorial interpretations of minimal free resolutions have been given in both cases. In this present work, we will generalize existing techniques to obtain two new results. The first is S[Λ]-resolutions of Λ-invariant submodules of k[Z] where Λ i...

We introduce the notion of interval valued intutionistic (S,T)-fuzzy left h-ideal (k-ideal) of a hemiring (semiring). We describe some characteristic properties and connections. Finally, we construct some equivalence relations induced by interval valued intutionistic (S,T)-fuzzy left h-ideals (k-ideals).

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk  have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...

Let K be a field and let G be a group. If G acts on an abelian group V , then it acts naturally on any group algebra K[V ], and we are concerned with classifying the G-stable ideals of K[V ]. In this paper, we consider a rather concrete situation. We take G to be an infinite locally finite simple group acting in a finitary manner on V . When G is a finitary version of a classical linear group, ...

A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet Σ such that L = LΣ∗ (L = Σ∗L, L = Σ∗LΣ∗). Let k = 3 for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences (Ln | n > k) of right, left, and two-sided regular ideals, where Ln has quotient complexity (state complexity) n, such that Ln is most complex in its class und...

The Hilbert series of local cohomologies for monomial ideals, which are not necessarily square-free, is established. As applications, we give a sharp lower bound of the non-vanishing degree of local cohomologies and also a sharp lower bound of the positive integer k of k-Buchsbaumness for generalized CohenMacaulay monomial ideals.

The Mycielski ideal Mk is defined to consist of all sets A ⊆ k such that {f ↾ X : f ∈ A} 6= k for all X ∈ [ω]0 . It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Ros lanowski ideals will be shown to be consistently different.

The goal of local class field theory is to classify abelian Galois extensions of a local field K. Several definitions of local fields are in use. In this thesis, local fields, which will be defined explicitly in Section 2, are fields that are complete with respect to a discrete valuation and have a finite residue field. A prototypical first example is Qp, the completion of Q with respect to the...

It gives a class of p-Borel principal ideals of a polynomial algebra over a field K for which the graded Betti numbers do not depend on the characteristic of K and the Koszul homology modules have monomial cyclic basis. Also it shows that all principal p-Borel ideals have binomial cycle basis on Koszul homology modules.