arXiv subjects

Khalid Ouarghi

Publications and source records attributed to Khalid Ouarghi.

3 recordsLinked to original sources

arXiv2021

On global defensive k-alliances in zero-divisor graph of finite commutative rings

The global defensive $k$-alliance is a very well studied notion in graph theory, it provides a method of classification of graphs based on relations between members of a particular set of vertices. In this paper we explore this notion in zero-divisor graph of commutative rings. The established results generalize and improve recent work by Muthana and Mamouni who treated a particular case for $k=-1$ known by the global defensive alliance. Various examples are also provided which illustrate and delimit the scope of the established results.

math.AC↗

arXiv2010

Rings over which all (finitely generated) strongly Gorenstein projective modules are projective

The main aim of this paper is to investigate rings over which all (finitely generated strongly) Gorenstein projective modules are projective. We consider this propriety under change of rings, and give various examples of rings with and without this propriety.

math.AC↗

arXiv2008

Gorenstein dimensions in trivial ring extensions

In this paper, we show that the Gorenstein global dimension of trivial ring extensions is often infinite. Also we study the transfer of Gorenstein properties between a ring and its trivial ring extensions. We conclude with an example showing that, in general, the transfer of the notion of Gorenstein projective module does not carry up to pullback constructions.

math.AC↗