We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...

The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing if a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the pro...

A bstract We investigate the reduction of Feynman integrals to master using Gröbner bases in a rational double-shift algebra Y which integration-by-parts (IBP) relations form left ideal. The problem reducing given family can then be solved once and for all by computing basis ideal formed IBP relations. demonstrate this explicitly several examples. introduce so-called first-order normal-form we ...

A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....

This paper investigates the principal competing visions of global politics that are currently advanced in the public discourse about globalization in opposition to the traditional state-centered perspective. The first part of the paper develops an analysis of ideal models as cultural resources that grounds the different reading of human bonds. The second part applies the notion of ideal models ...

Let K be a number field and q an integral ideal in OK. A result of Tatuzawa [11] from 1973, computes the asymptotic (with error term) for ideals with norm at most x class narrow ray group modulo q. This bounds term constant whose dependence on is explicit but not explicit. The aim this paper to prove fully bound term.

This is the first in a series of papers highlighting applications reduced and coreduced modules. Let $R$ be commutative unital ring $I$ an ideal $R$. We show that $I$-reduced $R$-modules $I$-coreduced provide setting which Matlis-Greenless-May (MGM) Equivalence Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist derived category setting. realise $I$-torsion...

This paper is about Hilbert modular forms on certain Hilbert modular varieties associated with a totally real field L. Let p be unramified in L. We reduce to the inert case and consider modular forms modulo p. We study the ideal of modular forms with q-expansion equal to zero modulo p, find canonical elements in it, and obtain as a corollary the congruences for the values of the zeta function o...

In this paper, we present a new approach for computing normal forms in the quotient algebra A of a polynomial ring R by an ideal I. It is based on a criterion, which gives a necessary and suucient condition for a projection onto a set of polynomials, to be a normal form modulo the ideal I. This criterion does not require any monomial ordering and generalizes the Buchberger criterion of S-polyno...