Narrow Results

In this paper, we investigate commutativity of prime rings $R$ with involution ∗ of the second kind in which generalized derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Furthermore, we provide an example to show that the restriction imposed on the involution is not superfluous.

In this paper, we investigate permutation identities satisfied by semigroup left ideals and weak semigroup left ideals in prime nearrings. We obtain results on commutativity of multiplication and addition using these identities. We provide examples to show the necessity of certain conditions in some of the results obtained. Finally, we give a characterization of Galois field in terms of permutation identities.

In this paper, we show that some additive mappings of a Banach algebra are derivations. Moreover, we exhibit some commutativity criteria for a prime Banach algebra ${𝒜}$ admitting a derivation satisfying certain algebraic identities.

In this paper we investigate commutativity of prime rings with involution ∗ of the second kind in which endomorphisms satisfy certain algebraic identities. Furthermore, we provide examples to show that the various restrictions imposed by the hypotheses of our theorems are not superfluous.

In this paper, we investigate generalized derivations satisfying certain differential identities on semigroup ideals of right near-rings and discuss related results. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

In this work, we propose a definition of comonotonicity for elements of $B{(H)}_{sa}$, i.e. bounded self-adjoint operators defined over a complex Hilbert space $H$. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of $B{(H)}_{sa}$ that generalizes quantum expectations. We characterize Choquet expectations as the real-valued functionals over $B{(H)}_{sa}$ which are comonotonic additive, $c$-monotone, and normalized.

We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.

There is a large body of evidence showing that the existence of a suitably-constrained derivation on a 3-prime near-ring forces the near-ring to be a commutative ring. The purpose of this paper is to study generalized semiderivations which satisfy certain identities on 3-prime near-ring and generalize some results due to [H. E. Bell and G. Mason, On derivations in near-rings, North-Holland Math. Stud.137 (1987) 31–35; H. E. Bell, On prime near-rings with generalized derivation, Int. J. Math. Math. Sci.2008 (2008), Article ID: 490316, 5pp; A. Boua and L. Oukhtite, Some conditions under which near-rings are rings, Southeast Asian Bull. Math.37 (2013) 325–331]. Moreover, an example is given to prove that the necessity of the 3-primeness hypothesis imposed on the various theorems cannot be marginalized.