EuDML | Browse

Page 1

Displaying 1 – 5 of 5

The First Isomorphism Theorem and Other Properties of Rings

Artur Korniłowicz, Christoph Schwarzweller (2014)

Formalized Mathematics

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 $\hat{𝐙}$

Jiří Močkoř (1984)

Archivum Mathematicum

The set of minimal distances in Krull monoids

Alfred Geroldinger, Qinghai Zhong (2016)

Acta Arithmetica

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 $a = u_{1} \cdot . . . \cdot u_{k}$ . 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.

James Hein (1982)

Mathematica Scandinavica

The tame degree and related invariants of non-unique factorizations

Franz Halter-Koch (2008)

Acta Mathematica Universitatis Ostraviensis

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 $ω$ -invariant. Finally we present a simple monoid which fails to be locally tame and yet has nice factorization properties.