关于ZP-凝聚环

发布时间：2018-11-26 11:05

【摘要】：给出ZP-凝聚环的概念,举例说明左ZP-凝聚环不一定是右ZP-凝聚环,并利用ZP-内射盖及ZP-平坦预包对ZP-凝聚环进行一系列的等价刻画,如R是左ZP-凝聚环,当且仅当ZP-平坦右R-模的直积是ZP-平坦右R-模,当且仅当任意右R-模有一个ZP-平坦预包.证明左ZP-凝聚环上的任意左R-模存在ZP-内射盖,并揭示若R是左ZP-凝聚环,则RR是ZP-内射模,当且仅当任意左R-模有一个满的ZP-内射盖,当且仅当任意右R-模有一个单的ZP-平坦预包.
[Abstract]:This paper gives the concept of ZP- condensate ring, illustrates that left ZP- coherent ring is not necessarily right ZP- coherent ring, and uses ZP- injective cover and ZP- flat prepackage to characterize ZP- condensate ring, for example, R is left ZP- condensate ring. If and only if the direct product of a ZP- flat right R -module is a ZP- flat right R-module if and only if any right R-module has a ZP- flat prepackage. It is proved that any left R-module on a left ZP- coherent ring has a ZP- injective cover, and it is shown that if R is a left ZP- coherent ring, then RR is a ZP- injective module if and only if any left R-module has a full ZP- injective cover. If and only if any right R-module has a single ZP- flat prepacket.
【作者单位】：西南科技大学理学院;绵阳师范学院数学与计算机科学学院;四川师范大学数学与软件科学学院;
【基金】：国家自然科学基金(11171240)
【分类号】：O153.3

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