On the dual of a finitely generated multiplication module II
On the product of a module by an ideal
Remarks on Blowing-Up Divisorial Ideals.
Rings with a theory of gretest common divisors.
S-divisible modules over domains.
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids
Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.
Semiprime factorizations in unions of Dedekind domains.
Semirigid GCD Domains.
Semivaluations and -groups
Some characterizations of v-domains and related properties
Some families of finite groups and their rings of invariants
Some remarks on Lorenzen -group of partly ordered groups
Special isomorphisms of preserving GCD and their use
On the ring of polynomials in n variables over a field special isomorphisms ’s of into are defined which preserve the greatest common divisor of two polynomials. The ring is extended to the ring and the ring of generalized polynomials in such a way that the exponents of the variables are non-negative rational numbers and rational numbers, respectively. The isomorphisms ’s are extended to automorphisms ’s of the ring . Using the property that the isomorphisms ’s preserve GCD it...
Subrings in trigonometric polynomial rings.
The First Isomorphism Theorem and Other Properties of Rings
Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial
The group of divisibility of
The set of minimal distances in Krull monoids
Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say . The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every...
The structure of an almost artinian module.
The tame degree and related invariants of non-unique factorizations
Local tameness and the finiteness of the catenary degree are two crucial finiteness conditions in the theory of non-unique factorizations in monoids and integral domains. In this note, we refine the notion of local tameness and relate the resulting invariants with the usual tame degree and the -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.
Unique factorization in non-atomic integral domains
In un UFD ogni elemento non unitario può essere espresso in modo unico nella forma dove è un elemento unitario, i sono primi non associati e ogni . Per studiare questa fattorizzazione in un ambito non atomico, si prende in esame un certo numero di generalizzazioni della potenza di un primo . Per numerose di queste generalizzazioni si prova che si ottiene una forma di fattorizzazione unica e la si mette in relazione, nel caso in cui è un dominio di integrità, con rappresentazioni di carattere...