r-ideals and m-k-ideals in inclines

T-Ideal AND Α-Ideal OF BP-ALGEBRAS

“…Furthermore, in 2022, Gemawati et al [6] explored the concepts of r-ideal and m-k-ideal in BN-algebra and examined their properties within homomorphism BN-algebra. Also, numerous papers pertaining to ideals in algebraic structures have been explored by researchers in references [7], [8], [9], [10] and [11].…”

On r-Ideals and m-k-Ideals in BN-Algebras

“…We start with some definitions and theories about B-algebra and BN-algebra. Then, we give the concepts of an r-ideal in a semigroup, and a k-ideal and m-k-ideal in an incline, as discussed in [1][2][3][4]6,10,11].…”

“…In 2016, M. A. Erbay et al defined the concept of an r-ideal in commutative semigroups (see [10]). Furthermore, M. M. K. Rao defined the concept of an r-ideal and m-k-ideal in an incline (see [11]). An incline is a non-empty set 𝑀 with two binary operations, addition In 2017, E. Fitria et al discussed the concept of prime ideals in B-algebras, which produces a definition and various prime ideals and their properties in B-algebras, including that a non-empty subset I is said to be ideal in a B-algebra X if it satisfies 0 ∈ X and if y ∈ I, x * y ∈ I applies to x ∈ I for all x, y ∈ X (see [6]).…”

“…In 2016, M. A. Erbay et al defined the concept of an r-ideal in commutative semigroups (see [10]). Furthermore, M. M. K. Rao defined the concept of an r-ideal and m-k-ideal in an incline (see [11]). An incline is a non-empty set M with two binary operations, addition (+) and multiplication (•), satisfying certain axioms.…”