2018/02/23 by Daniel D. Anderson, Muhammad Zafrullah, Anderson, Daniel D. +1
Mathematics · #13A15 #13G05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A15 #msc:13G05
paper · pdf · doi:10.48550/arxiv.1802.08353
arxiv created 2018/02/23 · arxiv updated 2018/02/26
Let ∗ be a finite character star operation defined on an integral domain D. Call a nonzero ∗ -ideal I of finite type a ∗ -homogeneous (∗ -homog) ideal, if I\subsetneq D and (J+K)∗ ≠ D for every pair D\supsetneq J,K⊇ I of proper ∗ -ideals of finite type. Call an integral domain D a ∗ -Semi Homogeneous Domain (∗ -SHD) if every proper principal ideal xD of D is expressible as a ∗ -product of finitely many ∗ -homog ideals. We show that a ∗ -SHD contains a family F of prime ideals such that (a) D=∩P∈ FDP, a locally finite intersection and (b) no two members of F contain a common non zero prime ideal. The ∗ -SHDs include h-local domains, independent rings of Krull type, Krull domains, UFDs etc. We show also that we can modify the definition of the ∗ -homog ideals to get a theory of each special case of a ∗ -SH domain.