Abstract We explored new algebra structures such as δ —algebra, δ —subalgebra and δ —ideal in this work. In addition, we study their fundamental characteristics and their connections with other algebras, such as d/ρ/BCK - algebras, d/ρ/BCK – subalgebras and d/ρ/BCK – ideals. Also, some examples to illustrate our notions are given. MSC (2010): 20G05, 20D06, 20B30, 20B35
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