Adel Alahmadi

LEAVITT PATH ALGEBRAS OF FINITE GELFAND–KIRILLOV DIMENSION

Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.

Modules which are invariant under monomorphisms of their injective hulls

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of R into R (N) R can be extended to R R . Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is quasi-injective. The following results are obtained: M is quasi-injective if and only if M is pseudo-injective and M 2 is CS. Furthermore, if M is a direct sum of uniform modules, then M is quasi-injective if and only if M is pseudo-injective. As a consequence of this it is shown that over a right Noetherian ring R , quasi-injective modules are precisely pseudo-injective CS modules.

Saudi-KAU Coupled Global Climate Model: Description and Performance

BackgroundA new coupled global climate model (CGCM) has been developed at the Center of Excellence for Climate Change Research (CECCR), King Abdulaziz University (KAU), known as Saudi-KAU CGCM.PurposeThe main aim of the model development is to generate seasonal to subseasonal forecasting and long-term climate simulations.MethodsThe Saudi-KAU CGCM currently includes two atmospheric dynamical cores, two land components, three ocean components, and multiple physical parameterization options. The component modules and parameterization schemes have been adopted from different sources, and some have undergone modifications at CECCR. The model is characterized by its versatility, ease of use, and the physical fidelity of its climate simulations, in both idealized and realistic configurations. A description of the model, its component packages, and parameterizations is provided.ResultsResults from selected configurations demonstrate the model’s ability to reasonably simulate the climate on different time scales. The coupled model simulates El Niño-Southern Oscillation (ENSO) variability, which is fundamental for seasonal forecasting. It also simulates Madden-Julian Oscillation (MJO)-like disturbances with features similar to observations, although slightly weaker.ConclusionsThe Saudi-KAU CGCM ability to simulate the ENSO and the MJO suggests that it is capable of making useful predictions on subseasonal to seasonal timescales.

Decomposition of singular matrices into idempotents

In this paper, we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey (Products of idempotent matrices. Linear Multilinear A. 1983) and Rao (Products of idempotent matrices. Linear Algebra Appl. 2009) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems. We also consider singular matrices over Bézout domains as to when such a matrix is a product of idempotent matrices.

On self-dual double negacirculant codes

Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. Exact counting formulae are derived for DN codes. The special class of length a power of two is studied by means of Dickson polynomials, and is shown to contain families of codes with relative distances satisfying a modified Gilbert-Varshamov bound.

On the lifted Zetterberg code

The even-weight subcode of a binary Zetterberg code is a cyclic code with generator polynomial

Long module skew codes are good

g(x)=(x+1)p(x)

\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}

g(x)=(x+1)p(x), where p(x) is the minimum polynomial over GF(2) of an element of order