In this thesis we introduce and study the concept of a TAF-ring: a ring whose ideals are fnite products of 2-absorbing ideals. Following Badawi [7], an ideal I of a commutative ring R is a 2-absorbing ideal if whenever a; b; c ϵ R and abc ϵ 2 I, then ab ϵ I or ac ϵ I or bc ϵ I.