In this paper, we consider the structure of the multiplicative semigroup of a residue class ring R/I of a commutative ring R with identity modulo its nonzero ideal I. For the general case, we investigate the H-classes, maximal subgroups and the structure of Reg(R/I) which is the set of regular elements of R/I. If R is any integral domain and if I is a product of powers of invertible maximal ideals, we show that R/I is an epigroup, every H*-class of R/I is a nil-extension of a group (:unipotent epigroup) and that R/I is a complete lattice of unipotent epigroups.
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