A Schreier Domain Type Condition II

作者：Ahmad Zaheer; Dumitrescu Tiberiu; Epure Mihai^*

来源：Algebra Colloquium, 2015, 22(spec01): 923-934.

DOI：10.1142/S1005386715000772

• Schreier domain
• star operation
• Prufer domain

Let D be an integral domain and * a star operation on D. We study the domains characterized by the following property: whenever I D AB with I,A,B nonzero ideals, there exist nonzero ideals H and J such that I* = (HJ)*, H* superset of A and J* superset of B. We call them *-sharp domains. We show that D is t-sharp if and only if D[X] is t-sharp if and only if D[X]N-v is d-sharp, where N-v is the multiplicative set of D[X] consisting of all nonzero polynomials a(0) + a(1)X + ... + a(n)X(n) such that (a(0), a(1), ..., a(n))(v) = D.

• 出版日期2015-12