# Arabian Journal of Mathematics

Arabian Journal of Mathematics > 2012 > 1 > 1 > 29-38

*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 small values....

Arabian Journal of Mathematics > 2012 > 1 > 1 > 127-137

Arabian Journal of Mathematics > 2012 > 1 > 1 > 17-27

*H*of a group

*G*, let Γ

_{ H }(

*G*) be the directed graph with vertex set

*G*such that

*x*is the initial vertex and

*y*is the terminal vertex of an edge if and only if

*x*≠

*y*and $${xy\in H}$$ . Furthermore, if $${xy\in H}$$ and $${yx\in H}$$ for some $${x,y\in G}$$ with

*x*≠

*y*, then

*x*and

*y*will be regarded as being connected by a single undirected...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 113-126

Arabian Journal of Mathematics > 2012 > 1 > 1 > 97-111

*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...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 47-52

*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-dimensional Prüfer domain ...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 63-67

*R*has a finitistic weak dimension ≤ 2. More precisely, this dimension is 0 if

*R*is locally IF, 1 if

*R*is locally semicoherent and not IF, and 2 in the other cases.

Arabian Journal of Mathematics > 2012 > 1 > 1 > 69-87

*V*over a field

*K*. Many complications encountered in more general settings do not appear at this first level. We will prove the basic properties of the algebraic entropy of linear transformations $${\phi:V \to V}$$ of vector spaces and its characterization as the rank...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 1-16

*τ*-factorization, reduced

*τ*-factorization and Γ-factorization. Let

*D*be an integral domain, $${D^{\sharp}}$$ the non-zero, non-units of

*D*, and

*τ*a symmetric relation on $${D^{\sharp}}$$ . For $${a\in D^{\sharp}, a=\lambda a_{1}\cdots a_{n},\lambda}$$ a unit, $${a_{i}\in D^{\sharp}, n\geq1,}$$...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 53-61

*S*where every set of lengths of the factorizations of each element in

*S*is bounded. In particular, we show the connection between the elements of Δ(

*S*) and the Betti elements of

*S*. We prove how the minimum and maximum element of Δ(

*S*) can be determined using the Betti elements of

*S*. This leads to a determination of when Δ(

*S*) is a singleton...

Arabian Journal of Mathematics > 2012 > 1 > 1 > 39-46

*R*-smash products for Hopf quasigroups is developed.

Arabian Journal of Mathematics > 2012 > 1 > 1 > 89-95

*t*-class semigroup of an integral domain is the semigroup of the isomorphy classes of the

*t*-ideals with the operation induced by

*t*-multiplication. This paper investigates integral domains with Boolean

*t*-class semigroup with an emphasis on the GCD and stability conditions. The main results establish

*t*-analogues for well-known results on Prüfer domains and Bézout domains of finite character.

Arabian Journal of Mathematics > 2012 > 1 > 2 > 149-158

Arabian Journal of Mathematics > 2012 > 1 > 2 > 251-265

Arabian Journal of Mathematics > 2012 > 1 > 2 > 227-239

Arabian Journal of Mathematics > 2012 > 1 > 2 > 219-226

Arabian Journal of Mathematics > 2012 > 1 > 2 > 191-194

*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.

Arabian Journal of Mathematics > 2012 > 1 > 2 > 195-218

*U*

_{ q }(

*f*(

*K*,

*H*)) (see Wang et al. in Commun Algebra 30:2191–2211, 2002). A new class of algebras is defined, which is denoted by $${\mathfrak{w}U^{d}_q.}$$ For

*d*= ((1, 1) | (1, 1)), denote $${\mathfrak{w}U^{d}_q}$$...

Arabian Journal of Mathematics > 2012 > 1 > 2 > 139-148

Arabian Journal of Mathematics > 2012 > 1 > 2 > 175-190

*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 semihypergroup where...