Characterizations Of PTW Domains

In this paper, we characterize PTW domains by using general staroperations. Firstly, we provide the definition of PTW domains and show theequivalent definition. We also indicate the relationship between PTW domainsand several other important domains. Especially, we use an example to showPTW domains are not TW domains. Moreover, we study the PTW-propertyin terms of localization. We prove that if R is a v-coherent domain, thenR is a PTW domain if and only if the localization of R is a PTW domain.Besides, we give the properties of the polynomial domains about PTW domains;Secondly, we characterize the pullback of PTW domains. Especially, we provethe equivalent relationship about R, D, T and M in I-Strong Minor constructionand II-Strong Minor construction. And we obtain the relationship aboutw-dim(R), w-dim(D), w-dim(T) and ht(M) in Strong Minor construction;Thirdly, we study the overring of PTW domains. We show a special overring ofPTW domains which keep PTW-property. We prove that let M is a maximalideal of R which is SV-stable, if R is a PTW domain, then so is (M : M).We indicate the w-global transforms, t-global transforms, t-?at overrings andgeneralized transforms of PTW domains. We show that if R is a PTW domain,and also a SM domain, then Rtg = K. And we obtain the equivalent conditionsbetween R is a PTW domain and the overrings which contained in w-globaltransforms is PTW domains. Moreover, we prove the equivalent conditionsbetween R is a PTW domain and t-?at overrings or generalized transforms isPTW domains. Finally, we give the definition of DT domains which are specialPTW domains, And we indicate the PT-property in terms of localization,pullback and overring.