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narnonsmikemnonsmipi'i
lujvo x1 is a zero-divisor partnered with element(s) x2 in structure/ring x3, where neither x1 nor x2 is the zero(-like) element in x3 Let structure x3 have commutative group substructure that we name as "additive" and let "0" denote the additive identity thereof in the structure x3. In the set underlying x3 there exist elements x1, x2 ≠ 0 in structure x3 such that x1*x2 = 0 in structure x3; the partnership aforementioned is thusly defined. See also: nonsmipi'i.
nonsmipi'i
lujvo x1 is a zero-divisor partnered with element(s) x2 in structure/ring x3 x1 and x2 are elements of the set underlying x3 and x1*x2=0 in this structure x3 (where "0" denotes the 'additive' identity of the structure ("addition" merely being (one of) its commutative group operation(s))); the aforementioned partnership is so defined. Unlike many textbook definitions, this definition still allows such 0 to itself be a zero-divisor ((so partnered) with any element in the set underlying x3) in x3. See also: narnonsmikemnonsmipi'i