Realization of graded monomial ideal rings modulo torsion

Biprojectivty of Banach algebras modulo an ideal

In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between t...

Ideal bases for graded polynomial rings and applications to interpolation

Based on a generalized algorithm for the division with remainder of polynomials in several variables, a method for the construction of standard bases for polynomial ideals with respect to arbitrary grading structures is derived. In the case of ideals with finite codimension, which can be viewed upon as a polynomial interpolation problem, an explicit representation for the interpolation space of...

Length One Ideal Extensions and Their Associated Graded Rings

Hereditary properties of amenability modulo an ideal of Banach algebras

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Poincaré Series of Monomial Rings

Let k be a field, let I be an ideal generated by monomials in the polynomial ring k[x1, . . . , xt] and let R = k[x1, . . . , xt]/I be the associated monomial ring. The k-vector spaces Tori (k, k) are N -graded. We derive a formula for the multigraded Poincaré series of R, PRk (x, z) = ∑ i≥0,α∈Nt dimk Tor R i,α(k, k)x z, in terms of the homology of certain simplicial complexes associated to sub...