DT Domains And α-, B-, C- Operation In Commutative Rings

In this paper , the ring concerned is commutative ring with identityelement . First , we characterize DT domains by using general star operations .We illustrate that R is DT domain , if and only if every ideal of R is v-ideal .When R is v-coherent , R is DT domain , if and only if for every multiplicativeset S in R , RS is DT domain , if and only if for every prime ideal P in R ,RP is DT domain , if and only if for every maximal ideal M in R , RM isDT domain . Then by citing examples , we claim neither TW domain norDW domain is DT domain . Under Milnor construction , we make out theequivalence between TW domain and DW domain . Moreover , we prove thaton the condition of Milnor construction , if R is DT domain , D and T areboth DT domain . Second , we introduce a- , b- , c- operation via annihilator .Let S be a multiplicative set of R and I is a finitely generated ideal of R , weprove that (AnnI)S = AnnIS , and (Ia)S (?) ((Ia)S)a = (IS)a . Besides , anymaximal ideal of R is c-ideal , if and only if ef(R) = {R} , if and only if everyideal of R is c-ideal . Finally , we concentrate on studying a-ring , b-ring ,ba-ring . We explain that if R is a-ring , R is semi-local-ring . When R haveQ-property and R is b-ring , RS is also b-ring . Moreover , we illustrate thatif R is ba-ring and I is an ideal of R , I is contained in only finitely maximalb-ideals of R.