On Derivations of BCC-algebras

International Journal of Pure and Apllied Mathematics, 2013

Recently an algebra based on proportional calculi was introdued by Tamilarasi and Mekalai in the year 2010 known as T M −algebras [3]. Kandaraj and Chandramouleeswaran [5] introduced the notion of derivation on d−algebras. In [6], we introduced the notion of derivations on TM-algebras. In this paper, we introduce the notion of t−derivation on TM-algebras. We study the properties of regular t−derivations on a TM-algebra and prove that the set of all t−derivations on a TM-algebra forms a semigroup under a suitable binary composition.

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introduced and then investigate their basic properties. In connection with the notion of homomorphism, the authors study how the image and the pre-image of fuzzy left (right) derivations BCC-ideals under homomorphism of BCC-algebras become fuzzy left (right) derivations BCC-ideals. Furthermore, the Cartesian product of fuzzy left (right) derivations BCC-ideals in Cartesian product of BCC-algebras is introduced and investigated some related properties.

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.

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.

International Journal of Scientific and Research Publications (IJSRP), 2019

We collect some important concepts on BCK,BCI and BCL-algebras which are useful to develop the main results in subsequent topics. The left-right m-derivation of a BCI-algebra is introduced, and some related properties are investigated. Using the idea of regular m-derivation , we give characterizations of a psemi-simple BCI-algebra .We introduce the useful properties of m-derivation in BCI-algebras and commutative and maximal ideals in BCK-algebras .

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.

International Journal of Contemporary Mathematical Sciences, 2020

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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.

The notion of left-right (resp. right-left) derivation of Balgebra is introduced and some related properties are investigated. Also the notion of derivation of 0-commutative B-algebra is studied and some of its properties are investigated.

In this note, we investigate some fundamental properties and prove some results on derivations of BCI-algebras.