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NEW SMARANDACHE ALGEBRAIC STRUCTURES

unpublished

Generally In R' any plane with equation x + y + z = a, where a is nonzero number. is not a linear space under the usual vector addition and scalar multiplication If we define new algebraic operations on the plane x + y + z = a it will become a linear space in R'. The aoditive iOentity of this linear space has nonzero components. The plane x + y + Z = a touches the x-axis at point A (a .0 ,0) • y-axis at point B (a,a,O) and Z-axIS at point C (O,G,a). Take triangle ABC as a fixed equilateral

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