Revistas académicas de la Universidad Católica del Norte
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On domination in the total torsion element graph of a module
No full textLet R be a commutative ring with non-zero unity and M be a unitary R-module. Let T(M) be the set of torsion elements of M. Atani and Habibi [6] introduced the total torsion element graph of M over R as an undirected graph T(Γ(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ T(M). The main objective of this paper is to study the domination properties of the graph T(Γ(M)). The domination number of T(Γ(M)) and its induced subgraphs T or(Γ(M)) and T of(Γ(M)) has been determined. Some domination parameters of T(Γ(M)) are also studied. In particular, the bondage number of T(Γ(M)) has been determined. Finally, it has been proved that T(Γ(M)) is excellent, domatically full and well covered under certain conditions
Periodic orbits of Linear flows on connected Lie groups
No full textOur main goal is to study the periodic orbits of linear flows on a real, connected Lie group. Since each linear flow φt has a derivation associated ?, we show that the existence of periodic orbits of φt is based on the eigenvalues of the derivation ?. From this, we study periodic orbits of a linear flow on noncompact, semisimple Lie groups, and we work with periodic orbits of a linear flow on a connected, simply connected, solvable Lie groups of dimension 2 or 3
On weakly (m, n)−closed δ−primary ideals of commutative rings
No full textLet R be a commutative ring with 1 ̸= 0. In this article, we introduce the concept of weakly (m, n)−closed δ−primary ideals of R and explore its basic properties. We show that a proper ideal I of R is a weakly (m, n)−closed γ ◦ δ−primary ideal of R if and only if I is an (m, n)−closed γ ◦ δ−primary ideal of R, where δ and γ are expansions ideals of R with δ(0) is an (m, n)−closed γ−primary ideal of R. Furthermore, we provide examples to demonstrate the validity and applicability of our results
On edge irregularity strength of different families of graphs
No full textEdge irregular mapping or vertex mapping h : V (G) → {1,2,3,...,s} is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wth(cd) = h(c) + h(d), ∀c, d ∈ V(G) and ∀cd ∈ E(G). Edge irregularity strength denoted by es(G) is a minimum positive integer used to label vertices to form edge irregular labeling. In this paper, we find exact value of edge irregularity strength of linear phenylene graph PHn, Bn graph and different families of snake graph
Study of multiplicative derivation and its additivity
No full textIn this paper, we modify the result of M. N. Daif [1] on multiplicative derivations in rings. He showed that the multiplicative derivation is additive by imposing certain conditions on the ring ℜ. Here, we have proved the above result with lesser conditions than M. N. Daif for getting multiplicative derivation to be additive
Subspace spanning graph topological spaces of graphs
No full textA collection of spanning subgraphs TS, of a graph G is said to be a spanning graph topology if it satisfies the three axioms: Nn, K0 ∈ TS where, n = |V (G)|, the collection is closed under any union and finite intersection. Let (X, T) be a topological space in point set topology and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y . In this paper we discusses the subspace spanning graph topology defined by the graph topology TS on a spanning subgraph H of G
K-Riesz bases and K-g-Riesz bases in Hilbert C∗-module
No full textThis paper is devoted to studying the K-Riesz bases and the K-g-Riesz bases in Hilbert C∗-modules; we characterize the concept of K-Riesz bases by a bounded below operator and the standard orthonormal basis for Hilbert C∗-modules H. Also We give some properties and characterization of K-g-Riesz bases by a bounded surjective operator and g-orthonormal basis for H. Finally we consider the relationships between K-Riesz bases and K-g-Riesz bases
k-Zumkeller Graphs through Splitting of Graphs
No full textLet G = (V,E) be a simple graph with vertex set V and edges set E. A 1−1 function f : V → N is said to induce a k-Zumkeller graph G if the induced edge function f ∗ : E → N defined by f ∗(xy) = f(x)f(y) satisfies the following conditions:
f ∗(xy) is a Zumkeller number for every xy ∈ E.
The total distinct Zumkeller numbers on the edges of G is k.
In this article, we compute k-Zumkeller graphs through the graph splitting operation on path, cycle and star graphs
Characterization of prime rings having involution and centralizers
No full textThe major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are the generalization of many known theorems. Finally, we provide some examples to show that the conditions imposed in the hypothesis of our results are not superfluous
On ∗-reverse derivable maps
No full textLet R be a ring with involution containing a nontrivial symmetric idempotent element e. Let δ : R → R be a mapping such that δ(ab) = δ(b)a∗ + b∗δ(a) for all a, b ∈ R, we call δ a ∗−reverse derivable map on R. In this paper, our aim is to show that under some suitable restrictions imposed on R, every ∗−reverse derivable map of R is additive