Generalized Affine Transformation Monoid of a Residue Class Ring

In this paper, we consider the generalized affine transformation monoid Gaff (A/I) of a residue class ring A/I of a commutative ring A with identity modulo its nonzero ideal I. For the general case, we investigate the Green's relations, Schutzenberger group for every D-class and, the structure of group H-classes, regular D-classes, the idempotent set E(Gaff (A/I)) and the regular element set Reg (Gaff (A/I)) of Gaff (A/I). If A is an integral domain and I a product of powers of invertible maximal ideals, we show that Gaff (A/I) is an epigroup, every R^⋆-classes of Gaff (A/I) is a nil-extension of a right group and that Gaff (A/I) is a complete lattice of nil-extensions of right groups.