Nizar El Idrissi

@uit.ac.ma

Ibn Tofail University

Nizar El Idrissi


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https://researchid.co/nizar-el-idrissi

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics
5

Scopus Publications

9

Scholar Citations

2

Scholar h-index

Scopus Publications

  • Almost Sure Linear Independence of Absolutely Continuous Hilbert Space-Valued Random Vectors with Respect to a Special Class of Hilbert Space Probability Measures
    Boletim Da Sociedade Paranaense De Matematica, 2025
  • Invertibility in partially ordered nonassociative rings
    Nizar El Idrissi, Hicham Zoubeir
    Proyecciones, 2025
    Invertibility is important in ring theory because it enables division and facilitates solving equations. Moreover, (nonassociative) rings can be endowed with an extra ''structure'' such as order and topology allowing more richness in the theory. The two main theorems of this article are contributions to invertibility in the context of partially ordered nonassociative rings \\textit{and} Hausdorff sequentially Cauchy-complete weak-quasi-topological nonassociative rings. Specifically, the first theorem asserts that the interval $]0,1]$ in any suitable partially ordered nonassociative ring consists entirely of invertible elements. The second theorem asserts that if $f$ is a suitably generalized concept of seminorm from a nonassociative ring to a partially ordered nonassociative ring endowed with Frink's interval topology, then under certain conditions, the subset of elements such that $f(1-a) < 1$ consists entirely of invertible elements. Part of the assumption of the second theorem is that of Hausdorff sequential Cauchy-completeness of the first ring under the topology induced by the seminorm $f$ (which takes values in a partially ordered nonassociative ring endowed with Frink's interval topology). Frink's interval topology is an example of a coarse locally-convex $T_1$ topology. Moreover, to our knowledge, the topology induced by a seminorm into a partially ordered nonassociative ring has never been introduced. Some additional facts, such as the fact that the topology on a nonassociative ring $R_1$ induced by a norm into a totally ordered associative division ring $R_2$ endowed with Frink's interval topology (or equivalently, with the order topology, since the order of $R_2$ is total) is a Hausdorff locally convex quasi-topological group with an additional separate continuity property of the product, are dealt with in the second section ''Preliminaries''.
  • Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets
    Nizar El Idrissi, Samir Kabbaj
    Boletim Da Sociedade Paranaense De Matematica, 2024
    A relaxation of the notion of invariant set, known as $k$-quasi-invariant set, has appeared several times in the literature in relation to group dynamics. The results obtained in this context depend on the fact that the dynamic is generated by a group. In our work, we consider the notions of invariant and 1-internally-quasi-invariant sets as applied to an action of a function $f$ on a set $I$. We answer several problems of the following type, where $k \\in \\{0,1\\}$: what are the functions $f$ for which every finite subset of $I$ is internally-$k$-quasi-invariant? More restrictively, if $I = \\mathbb{N}$, what are the functions $f$ for which every finite interval of $I$ is internally-$k$-quasi-invariant? Last, what are the functions $f$ for which every finite subset of $I$ admits a finite superset that is internally-$k$-quasi-invariant? This parallels a similar investigation undergone by C. E. Praeger in the context of group actions.
  • Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
    Nizar El Idrissi, Samir Kabbaj, Brahim Moalige
    Proyecciones, 2023
    If H is a Hilbert space, the non-compact Stiefel manifold St(n, H) consists of independent n-tuples in H. In this article, we contribute to the topological study of non-compact Stiefel manifolds, mainly by proving two results on the path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold. In the first part, after introducing and proving an essential lemma, we prove that ∩j∈J (U(j) + St(n, H)) is path-connected by polygonal paths under a condition on the codimension of the span of the components of the translating J-family. Then, in the second part, we show that the topological closure of St(n, H)∩S contains all polynomial paths contained in S and passing through a point in St(n, H). As a consequence, we prove that St(n, H) is relatively dense in a certain class of subsets which we illustrate with many examples from frame theory coming from the study of the solutions of some linear and quadratic equations which are finite-dimensional continuous frames. Since St(n, L2(X, μ; F)) is isometric to, FF(X, μ), n, this article is also a contribution to the theory of finite-dimensional continuous Hilbert space frames.
  • Independence, infinite dimension, and operators
    Nizar El Idrissi, Samir Kabbaj
    Moroccan Journal of Pure and Applied Analysis, 2023
    In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator T sending en to e n +1 for all n ∈ ℕ (where (e n ) n ∈ℕ is a sequence of vectors) guarantees that (e n ) n ∈ℕ is linearly independent if and only if dim{e n } n ∈ℕ = ∞. In this article, we recover this result as a particular case of a general order-theory-based model-theoretic result. We then return to the context of vector spaces to show that, if we want to use a condition like T(e i ) = e ϕ ( i ) for all i ∈ I where I is countable as a replacement of the previous one, the conclusion will only stay true if ϕ : I → I is conjugate to the successor function succ : n ↦n + 1 defined on ℕ. We finally prove a tentative generalization of the result, where we replace the condition T(e i ) = e ϕ ( i ) for all i ∈ I where ϕ is conjugate to the successor function with a more sophisticated one, and to which we have not managed to find a new application yet.

RECENT SCHOLAR PUBLICATIONS

  • The topology of finite and infinite-dimensional Stiefel manifolds
    N El Idrissi
    2026
  • Parametrized equivalence relation on the global class of morphisms of a category and frame-theoretic examples
    N El Idrissi
    arXiv preprint arXiv:2602.12363 , 2026
    2026
  • Intersections of translates of finite-dimensionally valued frame spaces are conditionally slice-full and almost slice-full
    N El Idrissi
    2026
  • Two Hornich-Hlawka-type and Gram matrix-based inequalities
    N El Idrissi, H Zoubeir
    arXiv preprint arXiv:2601.18768 , 2026
    2026
  • Probability measure annihilating all finite-dimensional subspaces
    N El Idrissi, H Zoubeir
    arXiv preprint arXiv:2512.21664 , 2026
    2026
  • Almost sure linear independence of absolutely continuous Hilbert space-valued random vectors with respect to a special class of Hilbert space probability measures
    NE Idrissi, H Zoubeir
    arXiv preprint arXiv:2502.18908 , 2025
    2025
    Citations: 1
  • Invertibility in partially ordered nonassociative rings
    NE Idrissi, H Zoubeir
    arXiv preprint arXiv:2405.16565 , 2024
    2024
  • Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets
    N El Idrissi, S Kabbaj
    Boletim da Sociedade Paranaense de Matemática 42, 1-21 , 2024
    2024
    Citations: 1
  • Étude de quelques aspects de l'espace des repères, de l'indépendance et des ensembles quasi-invariants
    N El Idrissi
    Université Ibn Tofail, Faculté des sciences, Kénitra, Maroc , 2023
    2023
  • Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
    N El Idrissi, S Kabbaj, B Moalige
    Proyecciones (Antofagasta) 42 (3), 571-597 , 2023
    2023
    Citations: 3
  • Independence, infinite dimension, and operators
    N El Idrissi, S Kabbaj
    Moroccan Journal of Pure and Applied Analysis 9 (1), 86 - 96 , 2023
    2023
    Citations: 4

MOST CITED SCHOLAR PUBLICATIONS

  • Independence, infinite dimension, and operators
    N El Idrissi, S Kabbaj
    Moroccan Journal of Pure and Applied Analysis 9 (1), 86 - 96 , 2023
    2023
    Citations: 4
  • Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
    N El Idrissi, S Kabbaj, B Moalige
    Proyecciones (Antofagasta) 42 (3), 571-597 , 2023
    2023
    Citations: 3
  • Almost sure linear independence of absolutely continuous Hilbert space-valued random vectors with respect to a special class of Hilbert space probability measures
    NE Idrissi, H Zoubeir
    arXiv preprint arXiv:2502.18908 , 2025
    2025
    Citations: 1
  • Functions with a maximal number of finite invariant or internally-1-quasi-invariant sets or supersets
    N El Idrissi, S Kabbaj
    Boletim da Sociedade Paranaense de Matemática 42, 1-21 , 2024
    2024
    Citations: 1
  • The topology of finite and infinite-dimensional Stiefel manifolds
    N El Idrissi
    2026
  • Parametrized equivalence relation on the global class of morphisms of a category and frame-theoretic examples
    N El Idrissi
    arXiv preprint arXiv:2602.12363 , 2026
    2026
  • Intersections of translates of finite-dimensionally valued frame spaces are conditionally slice-full and almost slice-full
    N El Idrissi
    2026
  • Two Hornich-Hlawka-type and Gram matrix-based inequalities
    N El Idrissi, H Zoubeir
    arXiv preprint arXiv:2601.18768 , 2026
    2026
  • Probability measure annihilating all finite-dimensional subspaces
    N El Idrissi, H Zoubeir
    arXiv preprint arXiv:2512.21664 , 2026
    2026
  • Invertibility in partially ordered nonassociative rings
    NE Idrissi, H Zoubeir
    arXiv preprint arXiv:2405.16565 , 2024
    2024
  • Étude de quelques aspects de l'espace des repères, de l'indépendance et des ensembles quasi-invariants
    N El Idrissi
    Université Ibn Tofail, Faculté des sciences, Kénitra, Maroc , 2023
    2023