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The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint operators is p roved.

摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质，尤其证明了共轭算子的闭性。

Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.

最后，作为应用，证明了每一纯投射左R-模在纯子模下封闭当且仅当每一纯内射左R-模在纯满像下封闭。

Every module is a submodule an injective module and a homomorphic image of a projective module.

任何模都是内射模的子模，也是投射模的同态像。

A second subnumber is calculated for the second number as the multiplicative inverse of the first number with respect to a second submodule (120) that equals the second prime number minus 1, the first submodule and the second submodule being relatively prime.

计算该第二数的一个第二子数做为该第一数的相对于一个第二子模数(120)的一个倍数逆数，该第二子模数等于第二质数减1，第一子模数与第二子模数互质。

If N is a nonempty subset of a left R module M, then N is a submodule of M if and only if the following conditions hold:(1) x+y is in N for any element x,y in N;(2) rx is in N for any r in the ring R, and any x in N.

假设 N 是左模的非空子集合，那么N 是子模的充分必要条件是，对N 中的任何两个元素x，y有

In this paper the relationships of a prime submodule K of a right R-module M and its adjoint prime ideal adj=1 are investigated.

研究右R-模M的素子模K和它的伴随素理想adj＝之间的关系。

If you forget to publish the submodule change, others won't be able to clone the repository

如果你忘记了发布子模块的变动，其他人将无法克隆版本库

It's not safe to run git submodule update if you've made and committed changes within a submodule without checking out a branch first.

如果你并不是在首先提取一个分支的情况下运行 git submodule update 是不安全的。

To see how submodule support works, create four example repositories that can be used later as a submodule

既然知道了子模块已经至此了，创建四个样板版本库用作子模块。

If you want to make a change within a submodule and you have a detached head, then you should create or checkout a branch, make your changes, publish the change within the submodule, and then update the superproject to reference the new commit

如果你在子模块中进行了变动并且你处在剥离的头上，那么你应该创建或者是提取一个分支，作出你的更改，将这些更改发布到子模块中，并更新上级项目到一个新的交付引用。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。