<![CDATA[A non-empty set G with a binary operation ∗ and a constant 0 that satisfies the following axioms: , , and for all is called a BG-algebra. A non-empty subset I of G is said to be an ideal in G if it satisfies: (i) and (ii) and implies for all . This article introduces the new concept of r-ideal in BG-algebra, which is an extension of the ideal in BN-algebra. Unlike the definition of an ideal in BN-algebra, an r-ideal only requires a non-empty subset I of G without the need to satisfy the full ideal conditions. This study examines the properties of r-ideals and their relationships with subalgebras, normal, and ideals in BG-algebra. In the final part, it is concluded that every subalgebra is an r-ideal in BG-algebra, and every normal ideal is also an r-ideal.]]>
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