injective dimension meaning in English
单射维数
内射维数
Examples
- Weak injective module and weak injective dimension
弱内射模与弱内射维数 - In chapter 3 , we discuss n - flat modules and n - fp - injective modules , we define n - flat dimension and n - fp - injective dimension , we consider n - flat modules and n - fp - injective modules in commutative n - coherent rings , their properties are similar to flat and injectivc modules in commutative coherent rings
在第三章中，我们主要讨论了n -平坦模和n - fp内射模，定义了n -平坦维数和n - fp内射维数，并考虑了交换n -凝聚环中的n -平坦模和n - fp内射模。他们有类似于交换凝聚环中的平坦模和内射模的性质。 - At first a lot of new characterizations of gorenstein injective modules are given , then the author claim that a ring r is qf if and only if every left ( or right ) r - modules are gorenstein injective , and then show that if r is two - side noetherian , r is n - gorenstein if and only if every n - th cosyzygy of an injective resolution of a left ( and right ) r - module is gorenstein injective if and only if every n - th syzygy of an injective resolvent of a left ( and right ) right module is gorenstein injective . finally , we prove that for an n - gorenstein ring r with n > 0 , every module can be embedded in a gorenstein injective module and the injective dimension of its cokernel is at most n - 1
首先给出了gorenstein内射模的许多新的刻画，推出了环r是qf环当且仅当每个左(右)的r -模的单边内射分解式的第n个上合冲是gorenstein内射模，接着推出了左、右noether环只是n - gorenstein环当且仅当每个左(右)模的单边内射分解式的第n个上合冲是gorenstein内射模当且仅当每个左(右)模的单边内射预解式的第n合冲是gorenstein内射模，最后推出了n - gorenstein环中每个模都可嵌入到一个gorenstein内射模之中，且其上核的内射维数不大于n - 1 。