t-DERIVATIONS ON TM-ALGEBRAS

Recently an algebra based on propositional calculi was introdued by Tamilarasi and Mekalai in the year 2010 known as T M −algebras, see [6]. In our paper [1] we introduced the notion of derivation on TM-algebras. In this paper, we introduce the notion of symmetric bi-derivation on TM-algebras and study some of its properties.

In this paper, the notions of left-right (resp. right-left) t-derivations of BCC-algebras are studied and some properties on t-derivations of BCC-algebras are investigated. This paper also considers t-regular t -derivations and the d t -invariant on ideals of BCC-algebras.

Matematičnì studìï, 2022

The study's primary purpose is to investigate the A /T structure of a quotient ring, where A is an arbitrary ring and T is a semi-prime ideal of A. In more details, we look at the differential identities in a semi-prime ideal of an arbitrary ring using T-commuting generalized derivation. We prove a number of statements. A characteristic representative of these assertions is, for example, the following Theorem 3: Let A be a ring with T a semi-prime ideal and I an ideal of A. If (λ, ψ) is a non-zero generalized derivation of A and the derivation satisfies any one of the conditions: 1) λ([a, b]) ± [a, ψ(b)] ∈ T , 2) λ(a • b) ± a • ψ(b) ∈ T , ∀ a, b ∈ I , then ψ is T-commuting on I. Furthermore, examples are provided to demonstrate that the constraints placed on the hypothesis of the various theorems were not unnecessary.

2018

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB)+nδ(BA) = mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A) for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA⊕0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.

International Journal of Mathematics and Mathematical Sciences, 2013

The notion ofsymmetric left bi-derivationof aBCI-algebraXis introduced, and related properties are investigated. Some results on componentwise regular andd-regularsymmetric left bi-derivationsare obtained. Finally, characterizations of ap-semisimpleBCI-algebra are explored, and it is proved that, in ap-semisimpleBCI-algebra,Fis asymmetric left bi-derivationif and only if it is asymmetric bi-derivation.

Demonstratio Mathematica, 2014

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. I

2012

Motivated by some results on derivations in rings and derivations of BCI algebras recently we introduce the notion of derivations on d-algebras and f-derivations on d-algebras. In this paper we introduce the notion of left F-derivations of d-algebras and investigate some simple and interesting results.

Journal of Algebra and Its Applications, 2015

Let [Formula: see text] be an associative ring with center [Formula: see text] The objective of this paper is to discuss the commutativity of a semiprime ring [Formula: see text] which admits a derivation [Formula: see text] such that [Formula: see text] for all [Formula: see text] or [Formula: see text] for all [Formula: see text] or [Formula: see text] for all [Formula: see text] where [Formula: see text] and [Formula: see text] are fixed positive integers. Finally, we apply these purely ring theoretic results to obtain commutativity of Banach algebra via derivation.

International Journal of Contemporary Mathematical Sciences, 2020

This article is distributed under the Creative Commons by-nc-nd Attribution License.

arXiv (Cornell University), 2020

Suppose that X is a (real or complex) Banach space, dimX ≥ 2, and N is a nest on X , with each N ∈ N is complemented in X whenever N − = N. A ternary derivation of AlgN is a triple of linear maps (γ, δ, τ) of AlgN such that γ(AB) = δ(A)B + Aτ (B) for all A, B ∈ AlgN. We show that for linear maps δ, τ on AlgN there exists a unique linear map γ : AlgN → AlgN defined by γ(A) = RA + AT for some R, T ∈ AlgN such that (γ, δ, τ) is a ternary derivation of AlgN if and only if δ, τ satisfy δ(A)B + Aτ (B) = 0 for any A, B ∈ AlgN with AB = 0. We also prove that every ternary derivation on AlgN is an inner ternary derivation. Our results are applied to characterize the (right or left) centralizers and derivations through zero products, local right (left) centralizers, right (left) ideal preserving maps and local derivations on nest algebras.