In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroup using Grobner basis. We generalize the concept of homogeneous numerical ...

We show that the minimal number of generators and the Cohen-Macaulay type of a family of numerical semigroups generated by concatenation of arithmetic sequences is unbounded.

In this paper we derive some conditions for transversal intersection of polynomial ideals and present some examples. Finally, as an application of the results proved, we compute the Betti numbers of ideals of the form ...

We study a class of non-instantaneous impulsive fractional differential equations in a Banach space. We consider the Cauchy problem with Caputo derivative having variable lower limits and almost sectorial operators. We ...

We introduce the notion of star gluing of numerical semigroups and show that this preserves the arithmetically Cohen-Macaulay and Gorenstein properties of the projective closure. Next, we give a sufficient condition involving ...

Let q=|q|eiπθ be a nonzero complex number such that |q|≠1 and consider the compact quantum group Uq(2). For θ∉Q∖{0,1}, we obtain the K-theory of the underlying C⁎-algebra C(Uq(2)). We construct a spectral triple on Uq(2) ...

Let Fq[t] be the polynomial ring over the finite field Fq. For arithmetic functions ψ1,ψ2:Fq[t]→C, we establish that if a Bombieri-Vinogradov type equidistribution result holds for ψ1 and ψ2, then it also holds for their ...

Let a and d be two linearly independent vectors in N2, over the field of rational numbers. For a positive integer k≥2, consider the sequence a,a+d,…,a+kd such that the affine semigroup Sa,d,k=⟨a,a+d,…,a+kd⟩ is minimally ...