# Arabian Journal of Mathematics

## List of Papers (Total 201)

#### Nil-Armendariz rings relative to a monoid

For a monoid M, we introduce M-nil-Armendariz rings, which are generalizations of nil-Armendariz rings and M-Armendariz rings, and we investigate their properties. We show that every NI ring is M-nil-Armendariz for any unique product monoid M, and if R is a 2-primal and M-Armendariz ring, then R is M × N-nil-Armendariz, where N is a unique product monoid. Moreover, we study the...

#### Analysis of an influenza A (H1N1) epidemic model with vaccination

A nonlinear mathematical model for the spread of influenza A (H1N1) infectious diseases including the role of vaccination is proposed and analyzed. It is assumed that the susceptibles become infected by direct contact with infectives and exposed population. We take under consideration that only a susceptible person can be vaccinated and that the vaccine is not 100% efficient. The...

#### A note on zero-divisors of commutative rings

In this paper we show that if a ring R has finite Goldie dimension, then every finitely generated ideal of R consisting of zero-divisors has non-zero annihilator. We also construct an example of a ring of infinite Goldie dimension such that above condition does not hold.

#### Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the...

#### The maximal correlation for the generalized order statistics and dual generalized order statistics

In each of three exhaustive and distinct cases, it is found a distribution for which the correlation coefficient between the elements of the generalized order statistics (gos) is maximal. The corresponding result for the dual generalized order statistics (dgos) is derived for other three different distributions. Moreover, some interesting relations for the regression curves...

#### The 2-edge geodetic number and graph operations

For a connected graph G = (V, E) of order n ≥ 2, a set $${S\subseteq V}$$ is a 2-edge geodetic set of G if each edge $${e\in E - E(S)}$$ lies on a u-v geodesic with d(u, v) = 2 for some vertices u and v in S. The minimum cardinality of a 2-edge geodetic set in G is the 2-edge geodetic number of G, denoted by eg2(G). It is proved that for any connected graph G, β1(G) ≤ eg2(G...

#### Fundamental relations in simple and 0-simple semihypergroups of small size

We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple...

#### On the category of modules over some semisimple bialgebras

We study the tensor category of modules over a semisimple bialgebra H under the assumption that irreducible H-modules of the same dimension > 1 are isomorphic. We consider properties of Clebsch–Gordan coefficients showing multiplicities of occurrences of each irreducible H-module in a tensor product of irreducible ones. It is shown that, in general, these coefficients cannot have...

#### Almost principal ideals in R[x]

For an integral domain R with quotient field K, an upper-type ideal of R[x] is an ideal of the form $${I_f = f({\rm x})K[{\rm x}] \cap R[{\rm x}]}$$ for some polynomial $${f({\rm x}) \in K[{\rm x}] \backslash K}$$. Clearly, I f  = I rf for each nonzero $${r \in R}$$. Hence one can always choose f (x) from R[x]. Such an ideal I f is said to be almost principal if there is a...

#### Ascending the divided and going-down properties by absolute flatness

This paper aims to show that the “going-down ring” and the “divided ring” properties ascend along flat morphisms whose co-diagonal morphisms are flat, the so-called absolutely flat morphisms introduced by Olivier. But unibranchedness hypotheses are necessary as any henselization morphism shows. As a by-product, we get that the “unibranched divided ring” property is preserved by...

#### Does Int $${(\mathbb {Z})}$$ have the stacked bases property?

It is known that a Prüfer domain either with dimension 1 or with finite character has the stacked bases property. Following Brewer and Klinger, some rings of integer-valued polynomials provide, for every n ≥ 2, examples of n-dimensional Prüfer domains without finite character which have the stacked bases property. But, the following question is still open: does the two...

#### On injective and divisible modules

Divisible modules over general rings are considered and a general notion of divisibility is defined. In order to study these divisible modules we generalize the notion of injectivity. One consequence is that rings for which every principal right ideal is projective can be characterized. In addition, a characterization is given of when a submodule of a projective module is...