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Induced modules of strongly group-graded algebras

Th. Theohari-Apostolidi, H. Vavatsoulas (2007)

Colloquium Mathematicae

Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.

Inertial subrings of a locally finite algebra

Yousef Alkhamees, Surjeet Singh (2002)

Colloquium Mathematicae

I. S. Cohen proved that any commutative local noetherian ring R that is J(R)-adic complete admits a coefficient subring. Analogous to the concept of a coefficient subring is the concept of an inertial subring of an algebra A over a commutative ring K. In case K is a Hensel ring and the module A K is finitely generated, under some additional conditions, as proved by Azumaya, A admits an inertial subring. In this paper the question of existence of an inertial subring in a locally finite algebra is discussed....

Injective and projective properties of R [ x ] -modules

Sangwon Park, Eunha Cho (2004)

Czechoslovak Mathematical Journal

We study whether the projective and injective properties of left R -modules can be implied to the special kind of left R [ x ] -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.

Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4

Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)

Journal de Théorie des Nombres de Bordeaux

In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots. These...

Integer-valued polynomials on algebras: a survey

Sophie Frisch (2010)

Actes des rencontres du CIRM

We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature.

Integral closures of ideals in the Rees ring

Y. Tiraş (1993)

Colloquium Mathematicae

The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.

Intermediate domains between a domain and some intersection of its localizations

Mabrouk Ben Nasr, Noômen Jarboui (2002)

Bollettino dell'Unione Matematica Italiana

In this paper, we deal with the study of intermediate domains between a domain R and a domain T such that T is an intersection of localizations of R , namely the pair R , T . More precisely, we study the pair R , R d and the pair R , R ~ , where R d = ∩ R M ∣ M ∈ Max ⁢ R , h ⁢ t ⁢ M = dim ⁡ R and R ~ = ∩ R M ∣ M ∈ Max ⁢ R , h ⁢ t ⁢ M ≥ 2 . We prove that, if R is a Jaffard domain, then R , R d ⁢ n is a Jaffard pair, which generalize [5, Théorème 1.9]. We also show that if R is an S -domain, then R , R ~ is a residually algebraic pair (that is for each intermediate domain S between R and R ~ , if Q is a prime ideal of S ...

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