On universal derivations
On universal derivations
复制标题
关于普遍推导
DOI：
10.1016/0021-8693(75)90098-8
复制
发表时间：
1975
影响因子：
0.9
通讯作者：
Warren Dicks
中科院分区：
文献类型：
--
作者：
G. Bergman;Warren Dicks
设R是一个环，0：R-+ S，T：R-+ T环同态（8，T）-双模M，我们形成矩阵环I $ y），并研究R的表示，形式为r++，其中6是一个适当的映射R-+ M。（1）是环同态的充要条件是6是双模M上的（a，T）-导子.更一般地（定义和细节在第节考虑这样的映射在范畴的K-环的一个固定的环的条件是，那么6是一个导子零化K。假设给定的K-环的同态（T）和（7）分别有核Q和（6），我们想知道通过适当地选择M和（6）：R-+ M，映射（1）的核c可以有多小。显然我们总是有ab _C c _C和B。现在存在一个（S，T）-双凸映射，我们将cafi 92= l-WK '（S，T），具有一个泛导子d：-+ Sz; Lewin [8]指出，所需的最小核c是映射+（i 3）的核在某些假设下，他证明了下界c= ob实际上是由这个最小核实现的。第一作者得到了阿尔弗雷德·P·斯隆研究奖学金的支持，并在大部分工作完成的同时，是利兹大学环理论年（1972-1973）的嘉宾。第二作者得到了加拿大理事会博士奖学金W72 3425的支持。
Let R be a ring, and 0: R-+ S, T: R-+ T ring homomor (8, T)-bimodule M, we form the matrix ring I $ y), and look at representations of R, of the form r++ where 6 is an appropriate map R-+ M. The necessary and sufficient condition for (1) to be a ring homomorphism is that 6 be a (a, T)-derivat the bimodule M. More generally (definitions and details in Secti consider such maps in the category of K-rings for a fixed ring condition is then that 6 be a derivation annihilating K. Suppose the given homomorphisms (T and 7 of K-rings have kernels Q and 6, respectively, and we wish to know how small the kernel c of the map (1) can be made by appropriate choices of M and 6: R-+ M. Clearly we always have ab _C c _C an b. Now there exists an (8, T)-bi dule, which we shall cafi 92= l-WK’(S, T), with a universal derivation d:-+ Sz; and Lewin [8] pomts out that the desired minimal kernel c is the kernel of the map+(i 3 Under certain hypotheses he proves that the lower bound c= ob is in fact achieved by this minimal kernel.* The first author was supported by an Alfred P. Sloan research fellowship, and was a guest of the University of Leeds’ Ring Theory Year (1972-1973) while most of this work was done. The second author was supported by Canada Council Doctoral Fellowship W72 3425.