On Companion BN1-algebra

Annisa Mursalima; Sri Gemawati; Syamsudhuha.

doi:https://doi.org/10.14445/22315373/IJMTT-V66I6P529

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 6 | Year 2020 | Article Id. IJMTT-V66I6P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I6P529

On Companion BN1-algebra

Annisa Mursalima, Sri Gemawati, Syamsudhuha.

Abstract

BN-algebra is a non-empty set (X,*,0) satisfies the axioms (B1) x*x=0, (B2) x*0 = x and (BN) (x*y)*z=(0*z)*(y*x) for all x,y,z ε X. BN1-algebra is a BN-algebra that satisfies axiom (BN1) (x * y) * z = (0 * z) * (y * x). The operation Θ is called a subcompanion when satisfies ((x Θ y) * ) * y = 0 in BN1-algebra. The subcompanion operation Θ is said to be a comapanion if (z * x) * y = 0, then z * (x Θ y) =0. In this paper, we develop the formula definition of companion BN1-algebra. We also investigate the properties of companion BN1-algebra, such as being unique or singular and commutative with certain conditions.

Keywords

B-algebra, BN-algebra, BN1-Algebra, Companion.

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Citation :

Annisa Mursalima, Sri Gemawati, Syamsudhuha., "On Companion BN1-algebra," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 6, pp. 292-296, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I6P529