On (f,g)-derivations of G-algebras

Al-Kadi, Deena

doi:10.12988/pms.2017.7911

Cited by 1 publication

(2 citation statements)

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“…8) right cancellation law holds in Ⱬ therefore(14) becomes ф( )= .Similarly for * ф( )=0(15) by (P 3 ) equation (15) becomes * ф( )= * (16) by (P 8 ) left cancellation law holds in Ⱬ therefore (16) becomes ф( )= . Proposition 3.7:-Let ф be a (Right, Left)-derivation of an associative PU-algebra Ⱬ then (P 14 ): ф(0)= * ф( ), ∀ ∈ Ⱬ (P 15 ): ф is one-one map.…”

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confidence: 93%

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Characterization of Associative PU-algebras by the Notion of Derivations

Khan¹,

Khan²,

Aalm³

2021

AJMCM

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In this manuscript we insert the concept of derivations in associative PU-algebras and discuss some of its important results such that we prove that for a mapping being a (Left, Right) or (Right, Left)-derivation of an associative PUalgebra then such a mapping is one-one. If a mapping is regular then it is identity. If any element of an associative PU-algebra satisfying the criteria of identity function then such a map is identity. We also prove some useful properties for a mapping being (Left, Right)-regular derivation of an associative PU-algebra and (Right, Left)-regular derivation of an associative PUalgebra. Moreover we prove that if a mapping is regular (Left, Right)-derivation of an associative PU-algebra then its Kernel is a subalgebra. We have no doubt that the research along this line can be kept up, and indeed, some results in this manuscript have already made up a foundation for further exploration concerning the further progression of PU-algebras. These definitions and main results can be similarly extended to some other algebraic systems such as BCH-algebras, Hilbert algebras, BFalgebras, J-algebras, WS-algebras, CI-algebras, SU-algebras, BCL-algebras, BP-algebras and BO-algebras, Z-algebras and so forth. The main purpose of our future work is to investigate the fuzzy derivations ideals in PU-algebras, which may have a lot of applications in different branches of theoretical physics and computer science.

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confidence: 93%

“…Later, Abujabal and Al-Shehri [13], defined a left derivations in BCI-algebras and investigated a regular left derivations. Zhan and Liu [14] studied f-derivations in BCI-algebras and proved some results. Muhiuddin and Alroqi [15,16] introduced the notions of (α, β)-derivations in a BCI-algebras and investigated related properties.…”

Section: Introductionmentioning

confidence: 99%