Resco and Small gave the first example of an affine Noetherian algebra which is not finitely presented. It shown that their has no finite-dimensional filtrations whose associated graded algebras are Noetherian, affirming prediction. A modification yields countable fields over ‘almost all’ (that is, a co-countable continuum of) lack such filtration, answer to question suggested by Irving derived.

Abstract In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in Noetherian local ring continues to be true for divisorial filtrations on two-dimensional normal excellent R , and Hilbert polynomial fiber cone filtration has function which is sum linear bounded function. We these theorems first studying asymptotic properties divisors resolution singula...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

We prove that every regular Gaussian polynomial over a locally Noetherian ring has invertible content ideal. We do this by first proving that Gaussian polynomials over an approximately Gorenstein local ring have principal content ideal. We also show over locally Noetherian rings that a regular polynomial f of degree n is Gaussian if c(fg) = c(f)c(g) for polynomials g of degree at most n. Introd...

An element a of a commutative ring R is nilregular if and only if x is nilpotent whenever ax is nilpotent. More generally, an ideal I of R is nilregular if and only if x is nilpotent whenever ax is nilpotent for all a ∈ I. We give a direct proof that if R is Noetherian, then every nilregular ideal contains a nilregular element. In constructive mathematics, this proof can then be seen as an algo...

We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.

Let S be a semigroup and K be a field. A K-space K[S], with basis S and with multiplication extending, in a natural way, the operation on S, is called a semigroup algebra. It remains an open problem to characterize semigroup algebras that are a prime Noetherian maximal order. In this thesis, we give an answer to the problem for a large class of cancellative semigroups and we illustrate these re...

Let J be a graded ideal in a not necessarily commutative graded k-algebra A = A0⊕A1⊕· · · in which dimk Ai <∞ for all i. We show that the map A→ A/J induces a closed immersion i : Projnc A/J → Projnc A between the non-commutative projective spaces with homogeneous coordinate rings A and A/J . We also examine two other kinds of maps between non-commutative spaces. First, a homomorphism φ : A → B...