A not necessarily noetherian local ring O is called regular if every finitely generated ideal I O possesses finite projective dimension. In the article localizations O = Aq, q ∈ SpecA, of a finitely presented, flat algebra A over a Prüfer domain R are investigated with respect to regularity: this property of O is shown to be equivalent to the finiteness of the weak homological dimension wdimO. ...

We consider minimal 1-factor covers of regular multigraphs, focusing on those that are 1-factorizations. In particular, we classify cubic graphs such that every minimal 1-factor cover is also a 1-factorization, and also classify simple regular bipartite graphs with this property. For r > 3, we show that there are finitely many simple r-regular graphs such that every minimal 1-factor cover is al...

This paper deals with vertex-magic total labellings of graphs. Earlier work by many authors has shown many infinite families of graphs to admit such labelings. The fact that many of these graphs are regular led MacDougall to conjecture that all non-trivial regular graphs are vertexmagic. Previously Gray and MacDougall showed that all odd-order rregular graphs (r ≥ 2) of order up to v = 19 are v...

Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is simple undirected whose vertex set two vertices x y are adjacent if only [x,y]≠r [x,y]≠−r. In this paper, we obtain expressions for degrees show that ΓRr neither regular nor lollipop noncommutative. We characterize noncommutative rings such tree, in particular star graph. It also shown ΓR1r ΓR2ψ(r) isomorphic R1 R...

The integrity of a graph G, I(G), is defined by I(G) = minS⊆V (G){|S| + m(G − S)} where m(G− S) is the maximum order of the components of G− S. In general the integrity of r-regular graph is not known [?]. We answer the following question for special regular graphs. For any given two integers p and r such that pr 2 is an integer, is there a r-regular graph, say G ∗, on p vertices having size q ...

In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z)=1$. In this paper, we prove Becker's conjecture in the best-possible form; we show that the rational function $R(z)$ can be...

We describe a general decomposition mechanism to express the derivation relation of a word rewriting system R as the composition of a (regular) substitution followed by the derivation relation of a system R′ ∪ D, where R′ is a strict sub-system of R and D is the Dyck rewriting system. From this decomposition, we deduce that the system R (resp. R) preserves regular (resp. context-free) languages...

AIMS To test the efficacy and safety of a chitosan pad for femoral haemostasis as an adjunct to manual compression. Haemostasis of the femoral artery after coronary angiography by manual compression is time consuming and uncomfortable for the patient. Closure devices are costly and do not reduce vascular complication rate. The HemCon(r) pad is used by the US army to control traumatic bleeding. ...

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...

A graph whose edges are labeled either as positive or negative is called a signed graph. A signed graph is said to be net-regular if every vertex has constant net-degree k, namely, the difference between the number of positive and negative edges incident with a vertex. In this paper, we analyze some properties of co-regular signed graphs which are net-regular signed graphs with the underlying g...