Abebaw Tilahun (PhD)Abebe Legesse2018-07-172023-11-042018-07-172023-11-042011-01http://etd.aau.edu.et/handle/123456789/8825Let be a field and given a polynomials inK(x1,x2,...Xn)2 K(X1X2......NK)], we can define an affine varieties in and ideals in a polynomials ring1 ,2 ,. . .]. This project considers the polynomial functions on a variety. The algebraic properties of polynomial functions on a variety yield many insights in to the geometric properties of the variety. The collection of polynomial functions from the variety to the field (or the coordinate ring ]) has the sum and product operations constructed using the sum and product operations in . The construction of the coordinate ring ] is a special case of the quotient ring In particular, we relate the quotient ring 2 ,…,)⁄ to the ring] of polynomial functions on . And the relation between two isomorphic varieties and two coordinate rings of an affine varieties are consideredenOn Polynomial Functions on a VarietyThesis