On Commutativity of Rings with Generalized Derivations

The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R &#8594; R satisfying F(xy) = F(x)y + xd(y) for all x, y &#8712; R, where d is a derivation on R, such a function F is said to be a generalized derivation. In the present paper we have discussed the commutativity of prime rings admitting a generalized derivation F satisfying (i) [F(x), x] = 0, (ii) F([x, y]) = [x, y], and (iii) F(x &#9702; y) = x &#9702; y for all x, y in some appropriate subset of R.</p

Generalized Derivations with Commutativity and Anti-commutativity Conditions

Let R be a prime ring with 1, with char(R) &#8800; 2; and let F : R &#8594; R be a generalized derivation. We determine when one of the following holds for all x,y &#8712; R: (i) [F(x); F(y)] = 0; (ii) F(x)&#927;F(y) = 0; (iii) F(x) &#927; F(y) = x &#927; y .</p

On commutativity of semiprime Banach algebras

See PD

On Centralizing and Generalized Derivations Of prime Rings with involution

&nbsp;Let (R,∗) be a 2-torsion free ∗-prime ring with involution ∗, L= 0 be a nonzero square closed ∗-Lie ideal of R and Z the center of R. An additive mapping F: R −→ R is called a generalized derivation on R if there exists a derivation d: R−→Rcommutes with ∗ such that F(xy) = F(x)y +xd(y) holds for all x,y ∈ R. In the present paper, we shall show that L is contained in the center of R such that R admits a generalized derivations F and G with associated derivations d and g commute with ∗ satisfying several conditions

Assessing Gains of stakeholders for Mega Project implementation: Learning from Beneficiary Assessment of Lahore Ring Road Project, Pakistan

The population is increasing rapidly globally, and urban expansion of the cities has become an extensive trend in developing nations. Urban expansion patterns, such as transportation structure and road networks, affect transportation planning. This research was conducted on a mega project in Lahore city of Pakistan, i.e., the Lahore Ring Road (LRR) project. Limited research focused on the beneficiary assessment of the road project, and this research was carried out to fill this research gap. This research aims to evaluate the beneficiary assessment of DHA Phase 8 and Halloki Settlement along the Lahore Ring Road. The simple Random Sampling technique was used to conduct the household survey in the study area. This study concluded that most of the residents did not modify their houses nor increase the built-up area and height after the introduction of the project. This study inferred that the rental potential was high at some locations and low at old existing settlements. This research further concluded that community participation was ignored, and public facilities were not improved in the study area. But a project of LRR was very much beneficial and alive for the residents of Lahore city. Community participation should be enhanced in such types of megaprojects, and allied facilities in the nearby community should be upgraded. This research will be helpful for policymakers, urban planners, transportation planners, development authorities, and other stakeholders in planning future road projects in the country

Automorphisms with annihilator condition in prime rings

Let R be a prime ring, I a nonzero ideal of R, and a ∈ R. Suppose that σ is a nontrivial automorphism of R such that a{(σ(x ∘ y))n − (x ∘ y)m} = 0 or a{(σ([x,y]))n − ([x,y])m} = 0 for all x,y ∈ I, where n and m are fixed positive integers. We prove that if char(R) &gt; n + 1 or char(R) = 0, then either a = 0 or R is commutative