The A plus XB[X] construction from Prufer v-multiplication domains

JOURNAL OF ALGEBRA

卷:439

Article

Chang, Gyu Whan

关键词: A plus XB[X] construction;    PvMD;    Generalized GCD domain;    Multiplicative set of ideals;   

DOI  :  10.1016/j.jalgebra.2015.05.030

来源: Elsevier

【 摘 要 】

Let A subset of B be an extension of integral domains, X be an indeterminate over B, and R = A + XB[X]. We prove that if B is t-flat over A, then R is a PvMD if and only if A is a PvMD and B = A(G) for G a t-splitting set of ideals of A. We also prove that R is a GGCD domain if and only if A is a GGCD domain and B = A(G) for G a d-splitting set of ideals of A. Finally, we use this result to recover that R is a GOD domain if and only if A is a GOD domain and B = A(S) for some splitting set S of A. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free