H [n] = {(t1, . . . , tn) ∈ R n \ {0} | ∀j, [tj 6= 0 and t1 = t2 = · · · = tj−1 = 0] ⇒ tj > 0} ∪ {0}. LetM(H) denote the Banach algebra of all complex Borel measures with support contained in H, with the usual addition and scalar multiplication, and with convolution ∗, and the norm being the total variation of μ. It is shown that the maximal ideal space X(M(H)) of M(H), equipped with the Gelfan...

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J . Let F = {In}n≥0 be a good filtration of ideals in A. Denote by FJ (F) = ⊕ n≥0 (In/JIn)t n the fiber cone of F with respect to J. The paper characterizes the multiplicity and the CohenMacaulayness of FJ (F) in terms of minimal reductions of F .

It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic m× n matrix. In this paper we discuss the relations of t-minors for t < min(m,n). We will exhibit minimal relations in degrees 2 (non-Plücker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is...

Abstract Krull’s Maximal Ideal Theorem (MIT) is one of the most prominent incarnations Axiom Choice (AC) in ring theory. For many a consequence AC, constructive counterparts are well within reach, provided attention turned to syntactical underpinning problem at hand. This viewpoints revised Hilbert Programme commutative algebra, which will here be carried out for MIT and several related classic...

Given an iterated skew polynomial ring C[y1; τ1, δ1] . . . [yn; τn, δn] over a complete local ring C with maximal ideal m, we prove, under suitable assumptions, that the completion at the ideal m+ 〈y1, y2, . . . , yn〉 is an iterated skew power series ring. When C is a field, this completion is a local, noetherian, Auslander regular domain with Krull, classical Krull and global dimension all equ...

We consider an homogeneous ideal I in the polynomial ring $$S=K[x_1,\dots ,$$ $$x_m]$$ over a finite field $$K={\mathbb {F}}_q$$ and set of projective rational points $${{\mathbb {X}}}$$ that it defines space {P}}}^{m-1}$$ . concern ourselves with problem computing vanishing $$I({{\mathbb {X}}})$$ This is usually done by adding equations {P}}}^{m-1})$$ to radical. give alternative more efficien...