广义最大公因子整环中的*-理想

*-Ideals in Generalized GGCD Domains

主要对GGCD整环中的w-理想与t-理想进行了研究,并讨论了GGCD整环与PVMD之间的联系.证明了R是GGCD整环当且仅当R是w-乘法封闭的PVMD,当且仅当R是t-乘法封闭的PVMD.此外,利用星型算子理论给出了GGCD整环与其多项式环及分式环之间的一些等价刻画.

In this paper, we study w-ideals and t-ideals in GGCD domains, and discuss the relationships between GGCD domains and PVMDs. It is proved that an integral domain R is a GGCD domain if and only if R is a w-multiplicatively closed PVMD, if and only if R is a t-multiplicatively closed PVMD. Moreover, we show some equivalent characterizations of GGCD domain with its polynomial ring and quotient ring by utilizing star operation theory.