This paper introduces Farey Recursive Functions and investigates their basic properties. are a special type of recursive function from the rationals to commutative ring. The recursion these functions is organized by graph. They arise naturally in study 2-bridge knots links.

Let R be a commutative ring with unity and M unitary module. Nil(M) the set of all nilpotent elements M. The entire element graph over is an undirected E(G(M)) vertex as any two distinct vertices x y are adjacent if only + ∈ Nil(M). In this paper we attempt to study domination in investigate number well bondage its induced subgraphs N(G(M)) Non(G(M)). Some parameters also studied. It has been s...

in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...

For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ A...

For any commutative ring R that is not a domain, there is a zerodivisor graph, denoted Γ(R), in which the vertices are the nonzero zero-divisors of R and two distinct vertices x and y are joined by an edge exactly when xy = 0. In [Sm2], Smith characterized the graph structure of Γ(R) provided it is infinite and planar. In this paper, we give a ring-theoretic characterization of R such that Γ(R)...

Abstract Let R be a finite commutative ring. We define co-unit graph, associated to ring , denoted by G nu ( ) with vertex set V )) = U ), where is the of units and two distinct vertices x y being adjacent if only + ∉ / ). In this paper, we investigate some basic properties integers modulo n, for different values n. find domination number, clique number girth